A246005 - OEIS

%I #25 Nov 16 2014 21:46:22

%S 3,3,5,0,17,5,3,3,19,3,5,0,3,5,7,3,313,13,349,3,5,19,127,0,4229,11,17,

%T 3,3,7,5,19,19,3,3,5,3,3,5,0,5,5,7,3,4421,7,7,17,3,3,19,3,17,17,3,23,

%U 7,3,3,0,43,0,5,5,3,13,1171,11,163,3,3,5,3,7,13,3,3,17,13,3,7,5,3,0,181,3,5,5,19,17,223

%N Least k such that ((2n+1)^k-1)/2n is prime, or 0 if no such k exists.

%C a(92) > 10000, a(93)..a(133) = {37, 3, 17, 5, 11, 31, 577, 271, 3, 19, 13, 3, 41, 137, 3, 281, 13, 7, 239, 0, 5, 11, 3, 113, 7, 7, 5, 17, 0, 3, 17, 5, 7, 19, 5, 23, 2011, 31, 5, 5, 13}, a(134) > 10000, a(135)..a(139) = {41, 37, 5, 5, 3}, a(140) > 10000, a(141)..a(150) = {29, 5, 3, 0, 13, 3, 17, 17, 113, 193}.

%F a(n) = A084740(2n+1).

%e a(23) = 127 because 2 * 23 + 1 = 47, (47^k-1)/46 is composite for k = 2, 3, ..., 126 and prime for k = 127.

%o (PARI) a(n) = {l=List([4, 12, 24, 40, 60, 62, 84]); for(q=1, 91, if(n==l[q], return(0))); k=1; while(k, s=((2*n+1)^prime(k)-1)/(2*n); if(ispseudoprime(s), return(prime(k))); k++)} \\ _Eric Chen_, Nov 14 2014

%Y Cf. A084740, A084742, A126659.

%K nonn

%O 1,1

%A _Eric Chen_, Nov 13 2014