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Integers m such that no prime exists of the form abs(k! - 3m - 1), abs(k! - 3m), or abs(k! - 3m + 1).
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%I #9 Dec 16 2024 22:18:21

%S 17,19,29,31,45,49,57,59,63,69,73,79,83,85,87,89,97,99,101,107,109,

%T 115,119,121,129,131,135,139,143,149,151,157,159,161,165,169,171,173,

%U 177,179,185,187,189,195,197,199,209,213,217,219,223,227,229,233,235,249,255,259

%N Integers m such that no prime exists of the form abs(k! - 3m - 1), abs(k! - 3m), or abs(k! - 3m + 1).

%C 3*a(n) are the indices of the middle terms in the triples of consecutive zeros in A125211. The middle index of most consecutive zero triples in A125211 is odd and is a multiple of 3.

%e Triplets of consecutive zeros in A125211: {50,51,52}, {56,57,58}, {86,87,88}, {92,93,94}, ...

%Y Cf. A125162, A125163, A125164, A125211, A125212.

%K nonn

%O 1,1

%A _Alexander Adamchuk_, Nov 23 2006

%E Edited and extended by _Max Alekseyev_, Feb 10 2010