A217377 - OEIS

%I #6 Oct 03 2012 18:24:31

%S 1,0,0,2,0,1,0,4,2,1,0,1,0,3,2,1,0,1,0,2,1,4,0,3,1,1,1,3,0,1,0,1,1,2,

%T 1,2,0,1,3,1,0,15,0,3,1,1,0,4,3,3008,1,1,0,2,1,1,4,1,0,3,0,1,1,2,2,1,

%U 0,1,3,1,0,1,0,2,2,1,1,4,0,2,1,4,0,5,2,8

%N a(n) is the smallest m>=0 such that ((5n+1)*6^m-1)/5 is prime; or -1 if no such value exists.

%C Let f(n)=6n+1. Let f(n,m) be f applied to n m-times. For example f(n,3) = f(f(f(n))). Then a(n) is the smallest m>=0 such that f(n,m) is prime.

%C a(525)=27871 is the largest found value in this sequence, which generates a probable prime with 21691 digits.

%C a(1247) and a(1898) are currently unknown. If they are positive then a(1247)>86500 and a(1898)>58000.

%H Dmitri Kamenetsky, <a href="/A217377/b217377.txt">Table of n, a(n) for n = 1..1246</a>

%e a(8)=4, because 4 is the smallest value for m such that ((5*8+1)*6^m-1)/5 is prime. The prime value is (41*6^4-1)/5 = 6*(6*(6*(6*8+1)+1)+1)+1 = 10627.

%Y Cf. A040081.

%K nonn

%O 1,4

%A _Dmitri Kamenetsky_, Oct 01 2012