Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I #11 Apr 01 2017 17:59:23
%S 30666137,3902132276156,2473929,1015214,464437,40743218950116,47,2344,
%T 61863,32660,4367,7974,11,2021170066180678,92343,784,571,2364594,13,
%U 20450,136113,2596,176011,262638,3223,512,59217,26,18973,6360528,23,11848,99,292226,832573
%N a(n) = (conjectured) smallest positive integer k which is neither of the form p + n^x nor of the form p - n^x with x >= 0 and p prime, where gcd(k, n) = 1 and gcd(k^2-1, n-1) = 1.
%C The definition is similar to that for A123159, but considering "p + n^x" and "p - n^x".
%C What does "conjectured" mean? A positive integer k is a candidate if:
%C 1) gcd(k, n) = 1,
%C 2) gcd(k^2-1, n-1) = 1,
%C 3) every term in the sequence k + n^x is divisible by one of the prime numbers of a covering set,
%C 4) all numbers of the form k - n^x are composite, k > n^x + 1, x >= 0.
%C The main problem is to prove that the given terms are indeed correct.
%C A quick search showed that a(8) = 47, a(14) = 11, a(20) = 13, a(27) = 512, a(29) = 26, a(32) = 23, a(34) = 99.
%C This is an interesting sequence: it leads to new classes of numbers. For example, the integer 30666137 is probably the smallest number that is simultaneously a Polignac number and a Sierpinski number.
%Y Cf. A076336, A123159, A263644, A283622.
%K nonn
%O 2,1
%A _Arkadiusz Wesolowski_, Mar 12 2017