A125164 - OEIS

%I #8 Sep 17 2024 21:07:35

%S 11,21,25,31,39,41,47,51,53,61,67,69,71,73,81,91,95,99,101,107,109,

%T 111,113,121,123,125,131,135,137,141,145,151,157,161,165,171,175,177,

%U 179,181,183,191,193,201,203,207,209,211,221,223,229,231,235,237,241,243,245,249,251,255,259

%N Positive integers n such that no prime exists of the form (k! + 3n - 1), (k! + 3n) or (k! + 3n + 1) for any k.

%C 3*a(n) is an index of the middle term in a triple of consecutive zeros in A125162. The indices of zeros in A125162 are listed in A125163.

%C Primes in this sequence form A115058.

%e Triplets of consecutive terms in A125163: {32,33,34}, {62,63,64}, {74,75,76}, {92,93,94}, {116,117,118}, {122,123,124}, {140,141,142}, {152,153,154}, {158,159,160}, {182,183,184}, {200,201,202}, {206,207,208}, {212,213,214}, {218,219,220}, {242,243,244}, {272,273,274}, {284,285,286}.

%Y Cf. A125162, A125163, A115058.

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Nov 22 2006

%E Edited and extended by _Max Alekseyev_, Feb 06 2010