0,1

All terms are primes. a(n) = 2 for n = {1,2,4,5,7,8,10,13,14,17,19,20,22,...} = A067076 Numbers n such that 2n+3 is a prime. a(34)-a(40) = {2,2,3,3,2,29,2}. a(42)-a(80) = {167,2,7,3,3,2,61,2,2,11,2,2,157,2,5,7,7,149,3,5,2,379,2,41,3,2,2,3,79,11,3,2,2,97,3,2,3,3,2}. a(82)-a(90) = {2,17,31,2,61,7,2,2,5}. a(93)-a(95) = {383,2,2}. a(97)-a(100) = {2,2,5,7}. a(102)-a(124) = {13,11,2,5,5,17,3,103,2,19,2,2,3,2,31,37,2,2,3,3,7,3,2}. a(127)-a(131) = {2,61,31,2,157}. a(133)-a(142) = {2,2,7,3,2,13,2,2,7,3}. a(144)-a(146) = {173,2,11}. a(148)-a(150) = {3,17,107}. a(n) is currently unknown for n = {33,41,81,91,92,96,101,125,126,132,143,147,...}.

Do[k = 1; While[ !PrimeQ[((2n+1)^k - 2^k)/(2n-1)], k++ ]; Print[k], {n, 100}] - Ryan Propper (rpropper(AT)stanford.edu), Mar 29 2007

Cf. A067076, Cf. A000043 = Primes p such that 2^p - 1 is prime. Cf. A001348 = Mersenne numbers: 2^p - 1, where p is prime. Cf. A057468 = numbers n such that 3^n - 2^n is prime. Cf. A125958 = Least number k>0 such that (2^k + (2n-1)^k)/(2n+1) is prime.

Sequence in context: A130451 A046027 A046028 this_sequence A122443 A099318 A091382

Adjacent sequences: A125951 A125952 A125953 this_sequence A125955 A125956 A125957

hard,nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Feb 07 2007

More terms from Ryan Propper (rpropper(AT)stanford.edu), Mar 29 2007