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%I #18 Jan 24 2018 03:32:34
%S 8,15,22,28,29,36,41,43,50,54,57,60,64,67,71,78,79,80,85,92,93,98,99,
%T 104,106,113,117,119,120,127,129,132,134,136,141,145,148,154,155,158,
%U 160,162,169,171,174,176,179,183,184,190,191,193,197,204,210,211,212
%N Numbers of the form 6*j*k+j+k for positive integers j and k.
%C Equivalently, numbers r such that 6*r+1 has a nontrivial factor == 1 (mod 6).
%C These numbers, together with numbers of the form 6*j*k-j-k (A070799) are the numbers s for which 6*s+1 is composite (A046954). If we also add in the numbers of the form 6*j*k+j-k (A046953), we get the numbers t such that 6*t-1 and 6*t+1 do not form a pair of twin primes (A067611).
%C If N is the set of natural numbers, then the set N-{A070043 U A070799} are the numbers k that make 6*k+1 prime. - _Pedro Caceres_, Jan 22 2018
%H Vincenzo Librandi, <a href="/A070043/b070043.txt">Table of n, a(n) for n = 1..9000</a>
%e 41 = 6*2*3 + 2 + 3. Equivalently, 6*41+1 = (6*2+1)*(6*3+1).
%t Select[Range[250], MemberQ[Mod[Take[Divisors[6#+1], {2, -2}], 6], 1]&]
%Y Cf. A070799, A046953, A046954, A067611.
%K nonn
%O 1,1
%A _Jon Perry_, May 05 2002
%E Edited by _Dean Hickerson_ and _Vladeta Jovovic_, May 07 2002
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