2,1

a(n) = A084740(n) for all n except n = p-1, where p is an odd prime, or A084740(n) = 2. All nonzero terms are odd primes. a(n) = 0 for n = {4,9,16,25,32,36,49,64,81,100,121,125,144,...}, which appears to be a union of the perfect squares k^2 for k>1 with the powers of primes p^k for k>1 with some exceptions, such as 2^3, 3^3, 2^7, etc. a(n) = 3 for n = {2,3,5,6,8,12,14,15,17,20,21,24,27,33,38,41,...} = A002384(n) for n>1, Numbers n such that n^2 + n + 1 is prime. a(19)-a(41) = {19,3,3,5,5,3,0,7,3,5,5,5,7,0,3,13,313,0,13,3,349,5,3}. a(43)-a(95) = {5,5,19,7,127,19,0,3,4229,103,11,3,17,7,3,41,3,7,7,3,5,0,19,3,19,5,3,29,3,7,5,5,3,41,3,3,5,3,0,23,5,17,5,11,7,61,3,3,4421,439,7,5,7}. a(97)-a(123) = {17,13,3,0,3,59,19,97,3,149,17,449,17,3,3,79,23,29,7,59,3,5,3,5,0,5,43}. a(125)-a(134) = {0,7,5,7,5,37,3,47,13,5}. a(136)-a(141) = {227,11,3,163,79,3}. a(143)-a(147) = {3,0,5,7,3}. a(n)>541 = Prime[100] is currently unknown for n = {18,42,96,124,135,142,148,...}.

H. Dubner, Generalized repunit primes, Math. Comp., 61 (1993), 927-930.

Eric Weisstein's World of Mathematics, Repunit

Cf. A084738, A065854, A084740 = Least k such that (n^k-1)/(n-1) is prime, or 0 if no such prime exists. Cf. A084741, A065507, A084742 = Least k such that (n^k+1)/(n+1) is prime, or 0 if no such prime exists.

Adjacent sequences: A128161 A128162 A128163 this_sequence A128165 A128166 A128167

Sequence in context: A084055 A084103 A036477 this_sequence A116580 A096439 A128046

hard,more,nonn

Alexander Adamchuk (alex(AT)kolmogorov.com), Feb 20 2007

a(18) = 25667 found by Henri Lifchitz, Sep 26 2007