[seqfan] Re: help needed editing A175625

[Vladimir Shevelev]

A definition is: Let m(n) be the n-th number such that 1) m(n)-1 is not multiple of 3, 2) 4^(m(n)+3)==1(mod(2*m(n)+7)), 3)4^(m(n)+2)==1 (mod (m(n)+3)). Then a(n)=2*m(n)+7.

E.g., m(1)=2 since 4^5==1(mod 11)  and 4^4==1(mod 5). Therefore, a(1)=2*m(1)+7=11.

Vladimir

----- Original Message -----
From: "N. J. A. Sloane" <njas at research.att.com>
Date: Saturday, July 31, 2010 21:28
Subject: [seqfan]  help needed editing A175625
To: seqfan at seqfan.eu
Cc: njas at research.att.com

> Dear Seq Fans,
> Could someone please study this sequence and provide a better 
> definition?Max Alekseyev, if you are around, it might help if
> you could ask the author in Russian exactly what the definition is.
> (I assume "compound" means "composite")
> 
> Thanks, Neil
> 
> The original sequence as submitted:
> 
> Date: Wed, 28 Jul 2010 09:51:59 -0400
> Subject: NEW SEQUENCE FROM submitN Alzhekeyev Ascar M A175625
> Reply-to: allasc at mail.ru
> 
> %I A175625
> %S A175625 11,23,31,47,59,83,107,167,179,227,263,347,359
> %N A175625 N(i)=2*i+7; ((2*i+7) mod 3)> 0; (N(i) does not share 
> on 3); 4 ^ (i+3) ��� 1 (mod (2*i+7)); 4 ^ (i+2) ��� 1 (mod 
> (i+3)) N(i) - primary number 
> %C A175625 N(i) - primary number 
> %C A175625 Then number N - idle time! It is checked up to N 
> <300 million. 
> %F A175625 N(i)=2*i+7; ((2*i+7) mod 3)> 0; (N(i) does not share 
> on 3); 4 ^ (i+3) ��� 1 (mod (2*i+7)); 4 ^ (i+2) ��� 1 (mod 
> (i+3)) 
> %F A175625 N(i) - primary number 
> %K A175625 nonn
> %O A175625 1,1
> %A A175625 Alzhekeyev Ascar M (allasc(AT)mail.ru), Jul 28 2010
> 
> My edited version (which probably did not make things better):
> 
> %I A175625
> %S A175625 11,23,31,47,59,83,107,167,179,227,263,347,359
> %N A175625 a(i)=2*i+7; ((2*i+7) mod 3)> 0; (a(i) does not share 
> on 3); 4^(i+3) == 1 (mod (2*i+7)); 4^(i+2) == 1 (mod (i+3)).
> %C A175625 Checked up to a <300 million.
> %K A175625 nonn,uned,new
> %O A175625 1,1
> %A A175625 Alzhekeyev Ascar M (allasc(AT)mail.ru), Jul 28 2010
> %E A175625 Partially edited by N. J. A. Sloane, Jul 29 2010
> 
> An update submitted via SubmitC.html:
> 
> Date: Fri, 30 Jul 2010 07:00:11 -0400
> Subject: COMMENT FROM submitC Alzhekeyev Ascar M A175625
> 
> START SUBMITC MESSAGE
> Sequence: A175625
> Sender: Alzhekeyev Ascar M
> Address: allasc at mail.ru
> Date of submission: Jul 30 2010
> 
> Description of changes, start:
> Description of changes, end
> 
> cdiff, start:
> *** /home/oeis/wwwfiles/sequences/tmp/tempC1.14292 Fri Jul 30 
> 07:00:11 2010
> --- /home/oeis/wwwfiles/sequences/tmp/tempC2.14292 Fri Jul 30 
> 07:00:11 2010
> ***************
> *** 2,7 ****
> --- 2,13 ----
>   %S A175625 11,23,31,47,59,83,107,167,179,227,263,347,359 
>   %N A175625 a(i)=2*i+7; ((2*i+7) mod 3)> 0; (a(i) does not 
> share on 3); 4^(i+3) == 1 (mod (2*i+7)); 4^(i+2) == 1 (mod 
> (i+3)). 
>   %C A175625 Checked up to a <300 million. 
> + %C A175625 30 Jul 2010 
> + %C A175625 The first compound number a(i)=536870911 
> + %C A175625 It is found by the user "venco" (from 
> http://dxdy.ru) 
> + %C A175625 It is interesting to notice that i+3=268435455=2^28-
> 1 
> + %C A175625 Please inform on a finding of following compound 
> numbers in sequence. 
> + %C A175625 Properties of number i+3 at exceptions (compound 
> numbers) are very interesting 
>   %K A175625 nonn,uned,new 
>   %O A175625 1,1 
>   %A A175625 Alzhekeyev Ascar M (allasc(AT)mail.ru), Jul 28 
> 2010 
> cdiff, end
> 
> Also a huge b-file arrived (with a different offset).
> 
> The present version is as follows:
> 
> %I A175625
> %S A175625 11,23,31,47,59,83,107,167,179,227,263,347,359
> %N A175625 a(i)=2*i+7; ((2*i+7) mod 3)> 0; (a(i) does not share 
> on 3); 4^(i+3) == 1 (mod (2*i+7)); 4^(i+2) == 1 (mod (i+3)).
> %C A175625 Checked up to a <300 million.
> %C A175625 The first compound number a(i)=536870911
> %C A175625 It is found by the user "venco" (from http://dxdy.ru)
> %C A175625 It is interesting to notice that i+3=268435455=2^28-1
> %C A175625 Please inform on a finding of following compound 
> numbers in sequence.
> %C A175625 Properties of number i+3 at exceptions (compound 
> numbers) are very interesting
> %H A175625 Alzhekeyev Ascar M, Table of n, a(n) for n = 2..11941610
> %K A175625 nonn,uned,new
> %O A175625 1,1
> %A A175625 Alzhekeyev Ascar M (allasc(AT)mail.ru), Jul 28 2010, 
> Jul 30 2010
> %E A175625 Partially edited by N. J. A. Sloane, Jul 29 2010
> 
> 
> 

 Shevelev Vladimir‎