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%I #8 Apr 16 2021 04:34:41
%S 1,2,10,16,28,34,36,40,46,50,51,52,56,57,58,64,66,70,76,78,82,86,87,
%T 88,92,93,94,96,100,106,112,116,120,124,126,130,134,135,136,142,144,
%U 146,147,148,154,156,160,162,166,170,171,172,176,177,178,184,186,188,189
%N a(n) = numbers n such that no prime exists of the form |k! - n|; or A125211(n) = 0.
%C Note the triples of consecutive zeros in A125211(n) for n = {{50,51,52}, {56,57,58}, {86,87,88}, {92,93,94}, ...}. Most zeros in A125211(n) have even indices. The middle index of most consecutive zero triples in A125211(n) is odd and is a multiple of 3. Numbers n such that no prime exists of the form (k! - 3n - 1), (k! - 3n), (k! - 3n + 1) are listed in A125213(n) = {17,19,29,31,45,49,57,59,63,69,73,79,83,85,87,89,97,99,...}. The first pair of odd middle indices of zero triples that are not divisible by 3 is n = 325 and n = 329. They belong to the first septuplet of consecutive zeros in A125211(n). A125211(n) = 0 for 7 consecutive terms from n = 324 to n = 330.
%H Amiram Eldar, <a href="/A125212/b125212.txt">Table of n, a(n) for n = 1..1000</a>
%e A125211(n) begins {0,0,2,3,2,1,3,2,2,0,5,1,7,1,1,0,9,1,6,1,2,1,4,1,2,1,1,0,5,1,8,1,1,0,2,0,10,1,1,0,6,1,10,1,1,0,10,1,3,0,0,0,7,...}.
%e Thus a(1) = 1, a(2) = 2, a(3) = 10, a(10)-a(12) = {50,51,52}.
%Y Cf. A125162 = number of primes of the form k! + n. Cf. A125163 = numbers n such that no prime exists of the form k! + n. Cf. A125164 = numbers n such that no prime exists of the form (k! + 3n - 1), (k! + 3n), (k! + 3n + 1). Cf. A125211, A125213.
%K nonn
%O 1,2
%A _Alexander Adamchuk_, Nov 23 2006
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