[seqfan] prime + factorial = prime

Leroy Quet q1qq2qqq3qqqq at yahoo.com
Mon Mar 1 22:22:19 CET 2010

I just submitted these two sequences.

%S A175193 1,2,2,3,2,3,2,4,3,2,3
%N A175193 a(n) = the smallest positive integer such that (the nth prime)+a(n)! is prime. 
%C A175193 A175194(n) = a(n)! 
%Y A175193 A092789,A175194 
%K A175193 more,nonn
%O A175193 1,2

%I A175194
%S A175194 1,2,2,6,2,6,2,24,6,2,6
%N A175194 a(n) = the smallest factorial such that (the nth prime)+a(n) is prime. 
%C A175194 a(n) = A175193(n)!. 
%Y A175194 A092789,A175193 
%K A175194 more,nonn
%O A175194 1,2

First, I know now I should have added the condition that
"a(n) = 0 if no such factorial (or positive integer) exists".

But, maybe not. Has it been proved that there is always a factorial m! such that a prime p plus m! = a prime?
As noted in the comment to sequence A092789, and which is obvious, m must be < p.

Second, the definition to A092789 seems to be completely wrong.
It seems what was meant was instead, a(n) = the smallest prime of the form p(n) + m!, where p(n) is the nth prime", or something like that.

In that case, the offset would be wrong too.

Leroy Quet

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