[seqfan] Sequence A037153
N. J. A. Sloane
njas at research.att.com
Thu Mar 4 20:28:30 CET 2010
Dear Seq Fans, the definition of A037153 is
%N A037153 a(n)=p-n!, where p is the smallest prime > n!+1.
That is, let p = smallest prime > n!+1, then a(n) = p - n!.
There is a comment saying:
%C A037153 Analogous to Fortunate numbers and like them, the entries appear to be primes. In fact, the first 541 terms are primes. Are all terms prime?
So there is a potentially different sequence, call it S, defined by:
Let p = smallest prime > n!+1 such that p - n! is also prime; then a(n) = p - n!
The other day Bob Wilson sent me a file called a037153.txt,
along with the following link:
%H A037153 Robert G. Wilson v (rgwv at rgwv.com), <a href="a037153.txt">Table of n, a(n) for n=1..120000</a> a(n) is the least prime such that n! + p is also prime. [From Robert G. Wilson v (rgwv(AT)rgwv.com), Mar 02 2010]
The file looks like this:
# This is the a037153.txt text file.
# A037153: a(n) is the least prime such that n! + p is also prime.
# Revised dated 02 March 2010.
1 2
2 3
3 5
4 5
...
1197 3643
1198 1619
1199 8599
1200 5393
There are several problems with this. 1. The file has only 1200 lines,
not 120000. 2. the statement
# A037153: a(n) is the least prime such that n! + p is also prime.
is wrong.
My guess is that this is a b-file for the sequence S. But there is a Mma
program in A037153 which does indeed produce the true A037153.
So I'm confused.
So I wonder if some sequence fan could produce a b-file for A037153.
Then either we will be able to update this remark:
%C A037153 Analogous to Fortunate numbers and like them, the entries appear to be primes. In fact, the first 541 terms are primes. Are all terms prime?
or we will get a counterexample, and we will have a new sequence S,
and a third sequence giving indices where they are different!
Bob, could you clarify what you did?
Neil
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