recycling A-numbers

[N. J. A. Sloane]

Leroy, Brendan:

Thanks for the warning.  It was risky, what I was doing
- although I was very careful only to merge the
most obscure sequences.

But the "A" in A-number stands for "Absolute", and to
be safe I won't do any more merging.

In fact I will restore the old duplicate sequences, just in
case there were any external links to them.

This is really very unlikely, becuase if anyone had ever
looked at any of these sequences they would have noticed
the duplication.

What I will do is restore the old sequence with its old A-number,
and make a short entry that points to the main entry.

So some of recent sequences will now be renumbered with
sequence numbers from the current A09**** range.  Of course i will
also update any links to them.

Let me show you a couple of examples, just to reassure
you that it was most unlikely there wewre links to these
sequences:

Example 1:

%I A081798
%S A081798 1,7,115,2371,54091,1307377,32803219,844910395,22188235867,591446519797,
%T A081798 15953338537885,434479441772845,11927609772412075,329653844941016785,
%U A081798 9163407745486783435,255982736410338609931,7181987671728091545787
%N A081798 Sum of three binomial coefficients.
%F A081798 y[n]= Sum[Binomial[n, k] Binomial[n + k, k] Binomial[n + 2k, k], {k, 0, n
}]
%Y A081798 Sequence in context: A084974 A064330 A086788 this_sequence A082487 A06339
9 A077394
%Y A081798 Adjacent sequences: A081795 A081796 A081797 this_sequence A081799 A081800
 A081801
%K A081798 easy,nonn
%O A081798 0,2
%A A081798 Emanuele Munarini (munarini(AT)mate.polimi.it), Apr 23 2003

same as

%I A082487
%S A082487 1,7,115,2371,54091,1307377,32803219,844910395,22188235867,591446519797,
%T A082487 15953338537885,434479441772845,11927609772412075,329653844941016785,
%U A082487 9163407745486783435,255982736410338609931,7181987671728091545787
%N A082487 Sum[ Binomial[n, k] Binomial[n + k, k] Binomial[n + 2k, k], {k, 0, n} ]
%Y A082487 Sequence in context: A064330 A086788 A081798 this_sequence A063399 A07739
4 A070067
%Y A082487 Adjacent sequences: A082484 A082485 A082486 this_sequence A082488 A082489
 A082490
%K A082487 easy,nonn
%O A082487 0,2
%A A082487 Emanuele Munarini (munarini(AT)mate.polimi.it), Apr 28 2003

Example 2:

%I A023347
%S A023347 831167,1154567,2502767,3019787,3675197,5056577,6352487,14519177,
%T A023347 26724377,43003577,47378927,47695607,56406197,86332457,86611757,99568757,
%U A023347 121967987,126435527,127990997,128149127,128975057,145281557,155715407
%N A023347 Remains prime through 5 iterations of function f(x) = 8x + 1.
%Y A023347 Sequence in context: A017611 A083618 A086128 this_sequence A063875 A01539
0 A043623
%Y A023347 Adjacent sequences: A023344 A023345 A023346 this_sequence A023348 A023349
 A023350
%K A023347 nonn
%O A023347 1,1
%A A023347 David W. Wilson (davidwwilson(AT)comcast.net)


and

%I A086128
%S A086128 831167,1154567,2502767,3019787,3675197,5056577,6352487,14519177,
%T A086128 26724377,43003577,47378927,47695607,56406197,86332457,86611757,
%U A086128 99568757,121967987,126435527,127990997,128149127,128975057,145281557
%N A086128 Remains prime through 5 iterations of function f[j]=8.f[j]+1, at f[1]=pri
me.
%F A086128 {p,8p+1,64p+9,512p+73,4096p+585,32768p+4681} are all primes, where p at t
he start is prime.
%e A086128 1st chain is: {831167,6649337,53194697,425557577,3404460617,27235684937};
%e A086128 If p is congruent {1,3,7,9} mod 10, then consecutive iterates are congrue
nt {9,5,7,3},{3,1,7,5},{5,9,7,1} respectively; so only 10k+7 may remain prime throug
h five iterations, as sequence demonstrates nicely.
%t A086128 k=0; m=8; Do[s=Prime[n]; s1=m*s+1; s2=m*s1+1; s3=m*s2+1; s4=m*s3+1; s5=m*
s4+1; If[PrimeQ[s]&&PrimeQ[s1]&&PrimeQ[s2]&&PrimeQ[s3] &&primeQ[s4]&&PrimeQ[s5], k=k
+1; Print[{k,n,s,s1,s2,s3,s4,s5}]],{n,1,1000000}]
%Y A086128 Cf. A085956, A086361, A086362, A023330, A059766, A086126, A000668, A07648
1, A086127.
%Y A086128 Sequence in context: A017479 A017611 A083618 this_sequence A023347 A06387
5 A015390
%Y A086128 Adjacent sequences: A086125 A086126 A086127 this_sequence A086129 A086130
 A086131
%K A086128 nonn
%O A086128 1,1
%A A086128 Labos E. (labos(AT)ana1.sote.hu), Jul 23 2003


(some of those lines did not mouse properly).



Anyway, I will restore all the A-numbers that I deleted or recycled.

They really are "absolute"!

Neil