# A139097 formula and extension correct?

Richard Mathar mathar at strw.leidenuniv.nl
Sun Jun 15 12:47:09 CEST 2008

Thankyou, Max.  It would be good to add the comment that these
are Gaussian Markov numbers.  Perhaps that will have to wait
until Alex Fink & I produce our paper?  And there are several
similar sequences which fall into the same category.  Some
examples are in Friday's message.       R.

On Sun, 15 Jun 2008, Maximilian Hasler wrote:

> old title "a(0) = 1, a(2) = 1; thereafter a(n) = 9 a(n-1) + a(n-2)"
> has a typo (a(2)), I suggest new title, give g.f., PARI & cite R.K.G's
> idea of extending to the left side.
>
> %I A015455
> %S A015455 1,1,10,91,829,7552,68797,626725,5709322,52010623,473804929,
> %T A015455 4316254984,39320099785,358197153049,3263094477226,29726047448083,
> %U A015455 270797521509973,2466903741037840,22472931190850533
> %N A015455 a(n) = 9 a(n-1) + a(n-2) for n>1; a(0) = a(1) = 1.
> %C A015455 Generalized Fibonacci numbers.
> %C A015455 As R.K.Guy suggested on the SeqFan list, the sequence could
> be extended "to the left side" by ..., 10, 1, 1, -8, 73, -665, 6058,
> -55187, 502741, -4579856, 41721445, ... by using the recurrence
> equation to get a(n-2) = a(n) - 9 a(n-1). The sequence 1,-8,73,...
> would have g.f. (1+x)/(1+9x-x^2).
> %H A015455 R. K. Guy, "A further family of sequences", SeqFan mailing
> list (www.seqfan.eu), Jun 13 2008
> %H A015455 Tanya Khovanova, <a
> href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive
> Sequences</a>
> %F A015455 g.f. = (1 - 8x)/(1 - 9x - x^2). - M.F.Hasler, Jun 14 2008
> %F A015455 a(n)=Sum_{k, 0<=k<=n} 8^k*A055830(n,k) .
>                - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Oct 18 2006
> %o A015455 (PARI) A015455(n) =
> polcoeff((1-(O(x^n)+8)*x)/(1-9*x-x^2),n) \\ - M.F.Hasler, Jun 14 2008
> %Y A015455 Sequence in context: A079928 A002452 A096261 this_sequence
> A110410 A051789 A015467
> %Y A015455 Adjacent sequences: A015452 A015453 A015454 this_sequence
> A015456 A015457 A015458
> %K A015455 nonn,easy
> %O A015455 0,3
> %A A015455 Olivier Gerard (ogerard(AT)ext.jussieu.fr)
> %E A015455 Edited by M.F.Hasler (www.univ-ag.fr/~mhasler), Jun 14 2008

Dear Seqfans,  A certain Juri-Stepan Gerasimov has submitted
a bunch of sequences but not using the web page.

This makes them much harder to edit - my editing program
processes submissions in the web page format.  These will
have to edited by hand.
I edited some of them myself, but I don't have time to
do the rest.

I have asked the author to use the web page, but he ignores my messages.

So I could use some help. Here are the messages that he sent me.

What needs to be done is to put them into the internal format.

Or of course to reject some of them, if they do not
(I could not understand some of the defintions,
but I did nopt spend any time on them.)

If someone is willing to do this, please post a note here, to
avoid duplication of effort.

Thanks!

Neil

From 2stepan at rambler.ru Tue Jun 10 04:29:31 2008

Estimble professor N.J.A.Sloane!

To send in a New Sequence

June 10 2008

New sequence (without an A-number):

5, 18, 30, 42, 29, 31, 78, 90, 53, 59, 61, 138, 73, 162, 89, 0, 198,
210, 222, 0, 0, 258, 137, 139, 149, 151, 157, 330, 173, 179, 181, 191,
390, 199, 0, 211, 0, 450, 462, 239, 241, 251, 257, 263, 269, 271, 558,
283, 293, 0, 0, 318, 630, 0, 0, 331, 337, 0, 347, 702

Definition of sequence:

A002476: -, 7, 13, 19, -, 31, 37, 43, -, -, 61, 67, 73, 79, -, -, 97,
103, 109, -, -, 127, -,  139

+

A007528: 5, 11, 17, 23, 29. -, 41, 47, 53, 59, -, 71, -, 83, 89,
-,101,107,113, -, -,131,137, -

=

198, 210, 222, 0, 0, 258,137, 139,

Index:

1

Formula:

-

References:

-

N.J.A.Sloane, Table of n,  a(n)  for  n = 0...200

http://ufkefl.narod.ru/primes

Example:

If  n =1,  then  a (1) = A002476(-) + A007528(1) = 0 + 5 = 5

If  n =11,  then  a (11) = A002476(7) + A007528(-) = 61 + 0 = 61

If  n =18,  then  a (18) = A002476(12) + A007528(14) = 103 +107 = 210

If  n = 21,  then  a (21) = A002476(-) + A007528(-) = 0 + 0 = 0

-

Program:

-

Cross-references:

Cf. A002476, A007528

Keywords:

nonn.

From 2stepan at rambler.ru Tue Jun 10 05:19:00 2008

Estimble professor N.J.A.Sloane!

To send in a New Sequence

June 10 2008

New sequence (without an A-number);

1, 3, 3, 3, 1, 2, 3, 3, 1, 1, 2, 3, 2, 3, 1, 0, 3, 3, 3, 0, 0, 3, 1, 2,
1, 2, 2, 3, 1, 1, 2, 1, 3, 2, 0, 2, 0, 3, 3, 1, 2, 1, 1, 1, 1, 2, 3, 2,
1, 0, 0, 3, 3, 0, 0, 2, 2, 0, 1, 3,

Definition of sequence:

A002476: -, 7, 13, 19, - , 31, 37, 43, -, -, 61, 67, 73, 79, -, -, 97,
103, 109, -, -, 127, -, 139

A007528: 5, 11, 17, 23, 29, -, 41-,47,53,59, -,71, -,83,89,
-,101,107,113, -, -, 131, 137, -

=

A002476:   0,  1,  1,  1,  0,  1,  1,  1,  0,  0,  1,  1,  1,  1,  0,
0,  1,  1,  1,  0,  0,  1,  0,  1

A007528:   1,  1,  1,  1,  1,  0,  1,  1,  1,  1,  0,  1,  0,  1,  1,
0,  1,  1,  1,  0,  0,  1,  1,  0

=

A ( new ) :   1,  3,  3,  3,  1,  2,  3,  3,  1,  1,  2,  3,  2,  3,  1,
0,  3,  3,  3,  0,  0,  3,  1,  2

Index:

1

Formula:

-

Referances:

-

N.J.A.sloane, Table of  n,  a (n)   for  n = 0...200

http://ufkefl.narod.ru/primes

Example:

-

Cjmments:

-

Program:

-

Cross-references:

Cf. A002476, A007528

Keywords:

nonn.

From 2stepan at rambler.ru Tue Jun 10 11:07:57 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 10 2008

New sequence (without an A-number)

For a new sequence:

6, 15, 5, 10, 14, 5, 10, 13, 5, 2, 15, 4, 2, 11, 1, 10, 6, 5, 12, 15, 0,
8, 7, 5, 8, 10, 5, 10, 12, 4, 2, 14, 0, 10, 3, 5, 2, 5, 5, 2, 9, 1, 8,
13, 5, 2, 14, 1, 2, 9, 5, 0, 12, 0, 10, 2, 5, 12, 2, 5, 12, 7, 0, 8, 14,
5, 8, 6, 4, 8

Definition of sequence:

A030430: -, 11, -, 31, 41, -, 61, 71,  -,  -, 101,  -,  -, 131, -, 151,
-,  -, 181, 191, -, 211, -, -,

A030431: 3,13, 23, -, 43, 53, -, 73, 83, -, 103, 113, -, -, -,
-,163,173,183,193, -, -,223,233

A030432: 7, 17, -, 37, 47, -, 67-, -, 97, 107, -, 127, 137, -, 157, 167,
-, -, 197, -, -, 227, -,

A030433: -, 19, 29,  -, -, 59, -, 79, 89, -, 109, -, -, 139, 149, -, -,
179, -, 199, -, -, 229, 239

=

A030430: 0,  1,  0,  1,  1,  0,  1,  1,  0,  0,  1,  0,  0,  1,  0,  1,
0,  0,  1,  1,  0,  1,  0,  0,

A030431: 1,  1,  1,  0,  1,  1,  0,  1,  1,  0,  1,  1,  0,  0,  0,  0,
1,  1,  1,  1,  0,  0,  1,  1,

A030432: 1,  1,  0,  1,  1,  0,  1,  0,  0,  1,  1,  0,  1,  1,  0,  1,
1,  0,  0,  1,  0,  0,  1,  0,

A030433: 0,  1,  1,  0,  0,  1,  0,  1,  1,  0,  1,  0,  0,  1,  1,  0,
0,  1,  0,  1,  0,  0,  1,  1,

=

A ( new ) : 6, 15, 5, 10, 14, 5,10,13, 5, 2, 15, 4, 2, 11, 1, 10, 6, 5,
12, 15, 0,  8,  7,  5

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ufkefl.narod.ru/primes

Example:

-

-

Program:

-

Cross-references:

Cf. A030430, AA030431, A030432, A030433

Keywords:

nonn.

From 2stepan at rambler.ru Thu Jun 12 10:03:20 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 10 2008

New sequence (without an A-number)

For a new sequence:

1, 32, 16, 129, 73, 36, 194, 6, 42, 176, 225, 12, 21, 89, 18, 97, 25,
243, 44, 44, 196, 34, 166, 90, 149, 152, 109, 66, 135, 224, 89, 169,
169, 28, 82, 210, 33, 213. 179, 170, 38, 92, 15. 96, 252, 171,

Definition of sequence:

A132236: 29, 59, 89, - , 149, 179, - , 239, 269, - , - , 359, 389, 419,
449, 479, 509, - , 569

A132235: 23, 53, 83, 113, - , 173, - ,  233, 263, 293, - , 353, 383,  -
, 443, - , 503,  - ,  563

A132234: 19,  - , 79, 109, 139,  - , 199, 229, - , - , - , 349, 379,
409, 439, - ,  499, - ,  - ,

A039919: 17, 47, - , 107, 137, 167, 197, 227, 257, - , 317, 347, - , - ,
- , 467, - , - , 557

A132233: 13, 43, 73, 103,  - , 163, 193, 223, - , 283, 313, - , 373, - ,
433, 463, - , 523, - ,

A132232: 11, 41, 71, 101, 131, - , 191, - , 251, 281, 311, - , - , 401,
431, 461, 491, 521, -,

A132231: 7, 37, 67,97,127,157,  - ,  - ,  - , 277, 307, 337, 367, 397, -
,457,487, - , - , 547,

A136066: -  , 31, 61,  - ,  - , 151,181,211,241,271, - , 331,  -  ,  -
, 421,  - ,  - ,  - , 541,

=

A132236:  0,   0,   0,   1,   0,   0,   1,   0,   0,   1,   1,   0,   0,
0,   0,   0,   0,   1,   0,

A132235:  0,   0,   0,   0,   1,   0,   1,   0,   0,   0,   1,   0,   0,
1,   0,   1,   0,   1,   0,

A132234:  0,   1,   0,   0,   0,   1,   0,   0,   1,   1,   1,   0,   0,
0,   0,   1,   0,   1,   1,

A039949:  0,   0,   1,   0,   0,   0,   0,   0,   0,   1,   0,   0,   1,
1,   1,   0,   1,   1,   0,

A132233:  0,   0,   0,   0,   1,   0,   0,   0,   1,   0,   0,   1,   0,
1,   0,   0,   1,   0,   1,

A132232:  0,   0,   0,   0,   0,   1,   0,   1,   0,   0,   0,   1,   1,
0,   0,   0,   0,   0,   1,

A132231:  0,   0,   0,   0,   0,   0,   1,   1,   1,   0,   0,   0,   0,
0,   1,    0,   0,   1,   0,

A136066:  1,   0,   0,   1,   1,   0,   0,   0,   0,   0,   1,   0,   1,
1,   0,   1,   1,   1,   0,

=

A ( new ) : 1. 32, 16, 129, 73, 36, 194, 6, 42, 176, 225, 12, 21, 89,
18, 97, 25, 243,

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ufkefl.narod.ru/primes

Example:

-

-

Program:

-

Cross-references:

Cf. A132236,A132235, A132234, A039919, A132233, A132232, A136066

Keywords:

nonn.

From 2stepan at rambler.ru Thu Jun 12 14:51:58 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 12 2008

New sequence (without an A-number)

For a new sequence:

1, 15, 57, 85, 99, 141, 155, 169, 183, 225, 253, 267, 281, 295, 309,
323, 351, 365, 393,407, 435, 449, 477, 505, 519, 533, 561, 575, 589,
603, 631, 645, 659, 687, 715, 729, 771, 785, 799, 813, 827, 841, 855,
869, 897, 925, 939, 981, 995,

Definition of sequence:

Nonprimes of form 14k+1

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ufkefl.narod.ru/primes

Example:

-

-

Program:

-

Cross-references:

Cf. A136062

Keywords:

nonn.

From 2stepan at rambler.ru Thu Jun 12 15:01:59 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 12 2008

New sequence (without an A-number)

For a new sequence:

9, 51, 65, 93, 121, 135, 177, 205, 219, 247, 261, 275, 289, 303, 345,
387, 415, 429, 471, 485, 513, 527, 555, 583, 597, 611, 625, 639, 667,
681, 695, 723, 737, 765, 779, 793, 807,

Definition of sequence:

Nonprimes of form 14k+9

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ufkefl.narod.ru/primes

Example:

-

-

Program:

-

Cross-references:

Cf. A045392

Keywords:

nonn.

From 2stepan at rambler.ru Thu Jun 12 15:39:22 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 12 2008

New sequence (without an A-number)

For a new sequence:

1, 22, 64, 85, 106, 148, 169, 190, 232, 253, 274, 295, 316, 358, 400,
421, 442, 484, 505, 526, 568, 589, 610, 652, 673, 694, 715, 736, 778,
799, 820, 841, 862, 904, 925, 946, 988, 1030, 1072, 1114, 1135, 1156,
1177, 1198, 1219, 1240, 1261, 1282, 1324, 1345, 1366, 1387, 1408, 1450,
1492

Definition of sequence:

Nonprimes of form 21k+1

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ufkefl.narod.ru/primes

Example:

-

-

Program:

-

Cross-references:

Cf. A136069

Keywords:

nonn.

From 2stepan at rambler.ru Fri Jun 13 06:59:00 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 13 2008

New sequence (without an A-number)

For a new sequence:

3, 4, 5, 5, 12, 13, 8, 15, 17, 20, 21, 29, 12, 35, 37, 9, 40, 41, 45,
48, 53, 11, 60, 61, 48, 55, 73, 39, 80, 89, 65, 72, 97, 20, 99, 101, 60,
91, 109, 15, 112, 113,

Definition of sequence:

Sequence of Pythagorean triangles (natural x, natural y, prime z)

Index:

1

Formula:

-

Referances:

Ìàëàõîâñêèé Â.Ñ. ×èñëà çíàêîìûå è íåçíàêîìûå. -- Êàëèíèíãðàä: ßíòàðíûé
ñêàç, 1998. -- 440 ñ.

http://www.research.att.com/~njfs/sequences/Submit.html

http://ufkefl.narod.ru/primes

Example:

-

-

Program:

-

Cross-references:

Cf. -

Keywords:

nonn.

From 2stepan at rambler.ru Fri Jun 13 07:24:30 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 13 2008

New sequence (without an A-number)

For a new sequence:

4, 3, 5, 12, 5, 13, 60, 11, 61, 180, 19, 181, 420, 29, 421,

Definition of sequence:

Sequence of Pythagorean triangles (natural x, prime y, prime z)

Index:

1

Formula:

x^2+y^2=z^2

Referances:

Ìàëàõîâñêèé Â.Ñ. ×èñëà çíàêîìûå è íåçíàêîìûå. -- Êàëèíèíãðàä: ßíòàðíûé
ñêàç, 1998. -- 440 ñ.

http://www.research.att.com/~njfs/sequences/Submit.html

http://ufkefl.narod.ru/primes

Example:

-

-

Program:

-

Cross-references:

Cf. -

Keywords:

nonn.

From 2stepan at rambler.ru Fri Jun 13 07:50:22 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 13 2008

New sequence (without an A-number)

For a new sequence:

3, 8, 5, 5, 24, 13, 7, 48, 20, 11, 120, 61, 13, 168, 85,

Definition of sequence:

Sequence of integer isosceles triangles (prime h, natural x, natural
y=z)

Index:

1

Formula:

S=(1/2)*h*x

Referances:

Ìàëàõîâñêèé Â.Ñ. ×èñëà çíàêîìûå è íåçíàêîìûå.-- Êàëèíèíãðàä: ßíòàðíûé
ñêàç, 1998. -- 440 ñ.

http://www.research.att.com/~njfs/sequences/Submit.html

http://ufkefl.narod.ru/primes

Example:

-

-

Program:

-

Cross-references:

Cf. -

Keywords:

nonn.

From 2stepan at rambler.ru Fri Jun 13 08:09:30 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 13 2008

New sequence (without an A-number)

For a new sequence:

4, 6, 5, 12, 10, 13, 24, 14, 25, 60, 22, 61,

Definition of sequence:

Sequence of integer isosceles triangles [h=2*p,  x=(1/2)*(p^2-1),
y=z=(1/2)*(p^2+1)]

Index:

1

Formula:

-

Referances:

Ìàëàõîâñêèé Â.Ñ. ×èñëà çíàêîìûå è íåçíàêîìûå. -- Êàëèíèíãðàä: ßíòàðíûé
ñêàç, 1998. -- 440 ñ.

http://www.research.att.com/~njfs/sequences/Submit.html

http://ufkefl.narod.ru/primes

Example:

-

-

Program:

-

Cross-references:

Cf.

Keywords:

nonn.

From 2stepan at rambler.ru Fri Jun 13 08:27:04 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 13 2008

New sequence (without an A-number)

For a new sequence:

3, 8, 5, 5, 24, 13, 15, 16, 17, 21, 40, 29, 35, 24, 37,

Definition of sequence:

Sequence of integer isosceles triangles [h=m^2-k^2,  x=4*m*k,  prime
y=z=p] and [p=m^2+k^2]

Index:

1

Formula:

-

Referances:

Ìàëàõîâñêèé Â.Ñ. ×èñëà çíàêîìûå è íåçíàêîìûå. -- Êàëèíèíãðàä: ßíòàðíûé
ñêàç, 1998. -- 440 ñ.

http://www.research.att.com/~njfs/sequences/Submit.html

http://ufkefl.narod.ru/primes

Example:

-

-

Program:

-

Cross-references:

Cf. -

Keywords:

nonn.

From 2stepan at rambler.ru Fri Jun 13 10:29:14 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 13 2008

New sequence (without an A-number)

For a new sequence:

Definition of sequence:

Lengths series nonprimes and primes congruent thus:

A136066:  - , 31, 61, - , - , 151, 181, 211, 241, 271, - , - , 331- , -
, 421, - , - , - , 541, 571,

+

A132231:  7, 37, 67, 97, 127, 157, - , - , - , 277, 307, 337, 367, 397,
- , 457, 487, - , 547,

+

A132232: 11, 41, 71, 101, 131, - , 191, - , 251, 281, 311, - , - , 401,
431, 461, 491, 521, - ,

+

A132233: 13, 43, 73, 103, - , 163, 193, 223, - , 283, 313, - , 373, - ,
433, 463, - , 523, - ,

+

A039919: 17, 47, - , 107, 137, 167, 197, 227, 257, - , 317, 347, - , - ,
- , 467, - , - , 557,

+

A132234: 19, - , 79, 109, 139, - , 199, 229, - , - , - , 349, 370, 409,
439, - , 499, - , - ,

+

A132235: 23, 53, 83, 113, - , 173, - , 233, 263, 293, - , 353, 383, - ,
443, - , 503, - , 563,

+

A132236: 29, 59, 89, - , 149, 179, - , 239, 269, - , - , 359, 389, 419,
449, 479, - , 569,

=

,79,83,89, -,97,101,103,107,109,113, - , - ,127,131, -,137,139,
-,149,151,157, -,163,167, -,173,179,181, -,191,193,197,199, -, -, -,
-,223,227,229,233,239,241, -,251, -,257, -,263,269,271,277,281,283, -,
-,293, -, -,307,311,313,317, -, -, -,331,337, -, -,347,349,353,359,
-,367, -,373, -,379,383,389, -,397,401, -, -,409, -,419,421, -,431,433,
-,439,443,449, -,457,461,463,467, -, -,479, -,487,491, -, -,499,503,509,
-,521,523, -, -, -, -,541,547, -,

=

A ( new ): 1, 12, 1, 6, 1, 3, 1, 6, 2, 2, 1, 2, 1, 3, 1, 2, 1, 3, 1, 4,
4, 5, 1, 1, 1, 1, 1, 6, 2, 1, 2, 4, 3, 2, 2, 4, 1, 1, 1, 1, 1, 3, 1, 2,
2, 1, 1, 2, 1, 2, 1, 3, 1, 4, 2, 1, 1, 2, 2, 3, 1, 2, 4, 2,

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ufkefl.narod.ru/primes

Example:

-

-

Program:

-

Cross-references:

Cf. A136066, A132231, A132232, A132233, A039919, A132234, A132235,
A132236

Keywords:

nonn.

From 2stepan at rambler.ru Fri Jun 13 11:55:31 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 13 2008

New sequence (without an A-number)

For a new sequence:

1, 15, 57, 85, 99, 141, 155. 169, 183, 225, 253, 267, 295, 309, 323,
351, 365, 393, 407, 435, 477, 505, 519, 533, 561, 575, 589, 603, 645,
687, 715, 729, 771, 785, 799, 813,

Definition of sequence:

Nonprimes of form 14k+1

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ufkefl.narod.ru/primes

Example:

-

-

Program:

-

Cross-references:

Cf. A136062

Keywords:

nonn.

From 2stepan at rambler.ru Fri Jun 13 12:03:54 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 13 2008

New sequence (without an A-number)

For a new sequence:

45, 87, 115, 129, 143, 171, 185, 213, 255, 297, 325, 351, 339, 381, 395,
423, 437, 451, 465, 493, 507, 535, 549, 591, 605, 633, 675, 689, 703,
717, 731, 745, 759, 801, 815,

Definition of sequence:

Nonrrimes of form 14k+3

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ufkefl.narod.ru/primes

Example:

-

-

Program:

-

Cross-references:

Cf. A045437

Keywords:

nonn.

From 2stepan at rambler.ru Fri Jun 13 12:17:22 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 13 2008

New sequence (without an A-number)

For a new sequence:

9, 51, 65, 93, 121, 135, 177, 205, 219, 247, 261, 275, 289, 303, 345,
387, 415, 429, 471, 485, 513, 527, 555, 583, 597, 611, 625, 639, 667,
681, 695, 723, 737, 765, 779, 793, 807,

Definition of sequence:

Nonprimes of form 14k+9

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ufkefl.narod.ru/primes

Example:

-

-

Program:

-

Cross-references:

Cf. -

Keywords:

nonn.

From 2stepan at rambler.ru Sat Jun 14 02:37:00 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 14 2008

New sequence (without an A-number)

For a new sequence:

3, 7, 7, 11, 13, 17, 19, 23, 37, 41, 43, 47, 67, 71, 79, 83, 97, 101,
103, 107, 109, 113, 127, 131, 163, 167. 193, 197, 229, 233, 277, 281,
307, 311, 313, 317, 349, 353, 379, 383, 439, 443, 457, 461, 463, 467,
487, 499, 503, 613, 617, 643, 647, 673, 677, 739, 743,

Definition of sequence:

List of primes (p, p+4)

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ufkefl.narod.ru/primes

Example:

-

-

Program:

-

Cross-references:

Cf. A000040

Keywords:

nonn.

From 2stepan at rambler.ru Sat Jun 14 02:47:40 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 14 2008

New sequence (without an A-number)

For a new sequence:

2, 3, 17, 3, 7, 257,

Definition of sequence:

List of triplet primes (p, 2^p -1, 2^2^p+1)

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ufkefl.narod.ru/primes

Example:

-

-

Program:

-

Cross-references:

Cf. A000040

Keywords:

nonn.

From 2stepan at rambler.ru Sat Jun 14 06:26:00 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 14 2008

New sequence (without an A-number)

For a new sequence:

7, 59, 137, 163, 241, 293, 397, 449, 631, 683, 709, 761, 787, 839, 1021,
1151, 1229,

Definition of sequence:

Primes of the form 26n+7

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ssd.sscc.ru/qt/primes.html

Example:

-

-

Program:

-

Cross-references:

Cf. A059245, A100202, A102732, A093191, A093350, A092178

Keywords:

nonn.

From 2stepan at rambler.ru Sat Jun 14 06:43:50 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 14 2008

New sequence (without an A-number)

For a new sequence:

61, 113, 139, 191, 269, 347, 373, 503, 607, 659, 919, 971, 997, 1049,
1153, 1231, 1283

Definition of sequence:

Primes of the form 26n+9

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ssd.sscc.ru/qt/primes.html

Example:

-

-

Program:

-

Cross-references:

Cf. A059245, A100202, A102732, A093191, A093350, A092178

Keywords:

nonn.

From 2stepan at rambler.ru Sat Jun 14 06:47:02 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 14 2008

New sequence (without an A-number)

For a new sequence:

11, 37, 89, 167, 193, 271, 349, 401, 479, 557, 661, 739, 947, 1051,
1103, 1129, 1181, 1259,

Definition of sequence:

Primes of the form 26n+11

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ssd.sscc.ru/qt/primes.html

Example:

-

-

Program:

-

Cross-references:

Cf. A059245, A100202, A102732, A093191, A093350, A092178

Keywords:

nonn.

From 2stepan at rambler.ru Sat Jun 14 06:50:00 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 14 2008

New sequence (without an A-number)

For a new sequence:

41, 67, 197, 223, 353, 379, 431, 457, 509, 587, 613, 691, 769, 821, 977,
1237, 1289,

Definition of sequence:

Primes of the form 26n+15

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ssd.sscc.ru/qt/primes.html

Example:

-

-

Program:

-

Cross-references:

Cf. A059245, A100202, A102732, A093191, A093350, A092178

Keywords:

nonn.

From 2stepan at rambler.ru Sat Jun 14 06:56:04 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 14 2008

New sequence (without an A-number)

For a new sequence:

23, 101, 127, 179, 257, 283, 439, 491, 569, 647, 673, 751, 829, 881,
907, 1063, 1193, 1297,

Definition of sequence:

Primes of the form 26n+23

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ssd.sscc.ru/qt/primes.html

Example:

-

-

Program:

-

Cross-references:

Cf. A059245, A100202, A102732, A093191, A093350, A092178

Keywords:

nonn.

From 2stepan at rambler.ru Sat Jun 14 07:35:00 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 14 2008

New sequence (without an A-number)

For a new sequence:

1, 27, 105, 183, 209, 235, 261, 287,  339, 365, 391, 417, 469, 495, 573,
625, 651, 703, 729, 755, 781, 807, 833, 885, 963, 989, 1015, 1041, 1067,
1119, 1145, 1197, 1275,

Definition of sequence:

Nonprimes of the form 26n+1

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ssd.sscc.ru/qt/primes.html

Example:

-

-

Program:

-

Cross-references:

Cf. A059245, A100202, A102732, A093191, A093350, A092178

Keywords:

nonn.

From 2stepan at rambler.ru Sat Jun 14 07:49:04 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 14 2008

New sequence (without an A-number)

For a new sequence:

Definition of sequence:

55, 81, 133, 159, 185, 237, 289, 315, 341, 393, 445, 471, 497, 549, 575,
627, 679, 705, 731, 783, 835, 861, 913, 939, 965, 1017, 1043, 1095,
1121, 1147, 1173, 1199, 1225, 1251,

Primes of the form 26n+3

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ssd.sscc.ru/qt/primes.html

Example:

-

-

Program:

-

Cross-references:

Cf. A100202

Keywords:

nonn.

From 2stepan at rambler.ru Sat Jun 14 07:59:45 2008

Estimble professor Neil J.A.Sloene!

To send in a New Sequence

June 14 2008

New sequence (without an A-number)

For a new sequence:

57, 135, 161, 187, 213, 265, 291, 343, 369, 395, 447, 473, 525, 551,
603, 629, 655, 681, 707, 759, 785, 837, 889, 915, 993, 1045, 1071, 1149,
1175, 1227, 1253,

Definition of sequence:

Nonprimes of the form 26n+5

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ssd.sscc.ru/qt/primes.html

Example:

-

-

Program:

-

Cross-references:

Cf.  A102732

Keywords:

nonn.

From 2stepan at rambler.ru Sat Jun 14 09:31:13 2008

Estimble professor Neil J.A.Sloane!

To send in a New Sequence

June 14 2008

New sequence (without an A-number)

For a new sequence:

69, 95, 121, 147, 225, 303, 329, 355, 381, 407, 459, 485, 511, 537, 589.
615, 687, 693, 745, 771, 849, 875, 901, 927, 979, 1005, 1057, 1083,
1135, 1161, 1239, 1265,

Definition of sequence:

Primes of the form 26n+17

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ssd.sscc.ru/qt/primes.html

Example:

-

-

Program:

-

Cross-references:

Cf. A093191

Keywords:

nonn.

From 2stepan at rambler.ru Sat Jun 14 09:43:20 2008

Estimble professor Neil J.A.Sloane!

To send in a New Sequence

June 14 2008

New sequence (without an A-number)

For a new sequence:

45, 123, 175, 201, 253, 279, 305, 357, 435, 513, 539, 565, 591, 679,
695, 721, 747, 799, 825, 851, 903, 955, 981, 1007, 1059, 1085, 1111,
1137, 1189, 1215, 1241, 1267,

Definition of sequence:

Primes of the form 26n+19

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ssd.sscc.ru/qt/primes.html

Example:

-

-

Program:

-

Cross-references:

Cf. A093350

Keywords:

nonn.

From 2stepan at rambler.ru Sat Jun 14 09:54:21 2008

Estimble professor Neil J.A.Sloane!

To send in a New Sequence

June 14 2008

New sequence (without an A-number)

For a new sequence:

Definition of sequence:

21, 99, 125, 177, 203, 255, 333, 385, 411, 437, 489, 515, 567, 645, 671,
697, 723,749, 775, 801, 879, 905, 931, 957, 1035, 1113, 1139, 1165,
1191, 1243, 1269, 1295,

Primes of the form 26n+21

Index:

1

Formula:

-

Referances:

-

http://www.research.att.com/~njfs/sequences/Submit.html

http://ssd.sscc.ru/qt/primes.html

Example:

-

-

Program:

-

Cross-references:

Cf. A092178

Keywords:

nonn.