cp's OEIS Frontend

A160433 a(n) is the least number k such that (k-th prime after n!+1)-n! is not a prime.

%I A160433 #5 Jul 06 2015 03:38:47
%S A160433 2,2,3,7,8,15,8,18,16,19,12,20,11,8,11,6,12,23,24,15,31,21,27,15,16,
%T A160433 26,25,17,17,29,20,27,27,30,23,16,28,23,25,29,15,24,19,36,36,39,15,36,
%U A160433 24,44,35,29,27,25,36,22,37,31,32,41,29,55,27,45,29,59,34,37,24,49,25,40
%N A160433 a(n) is the least number k such that (k-th prime after n!+1)-n! is not a prime.
%C A160433 The conjectures from A037153 and A087202 can be rephrased using a(n):
%C A160433 Is a(n)>=2 for all n>=0 and a(n)>=3 for all n>=2?
%C A160433 Also compare this with the conjecture on the fortunate numbers A005235.
%C A160433 Is the following true: for every m there is an N such that for all n>N a(n)>m?
%C A160433 There even seems to be the estimate a(n)>log(n+1)*sqrt(n+1)/2.
%e A160433 a(3)=7: The seven primes following 3!+1=7 are 11,13,17,19,23,29 and 31.
%e A160433 Subtracting 3!=6 from each of them gives 5,7,11,13,17,23 and 25.
%e A160433 The first six values are prime, while the seventh 25=5^2 is not.
%p A160433 a:=proc(n) option remember; local k:
%p A160433 for k from 1 while isprime((nextprime@@k)(n!+1)-n!) do od:
%p A160433 k; end;
%Y A160433 Cf. A005235, A037153, A087202.
%K A160433 nonn
%O A160433 0,1
%A A160433 Frederick Magata (frederick.magata(AT)web.de), May 13 2009