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Numbers n such that 12*n+7 is not prime.
1

%I #10 Sep 08 2022 08:45:48

%S 4,7,9,14,15,19,20,21,24,26,28,29,32,33,34,35,37,39,42,44,46,48,49,54,

%T 55,56,58,59,63,64,66,69,70,72,74,77,78,79,81,83,84,85,89,91,92,94,95,

%U 96,98,99,100,101,103,104,105,109,111,112,113,114,115,117,119,124,125

%N Numbers n such that 12*n+7 is not prime.

%H Vincenzo Librandi, <a href="/A166569/b166569.txt">Table of n, a(n) for n = 1..1000</a>

%e Distribution of the terms in the following triangular array:

%e *;

%e *,*;

%e *,*,*;

%e *,*,*,*;

%e *,4,*,*,*;

%e *,*,7,*,*,*;

%e *,*,*,*,*,*,*;

%e *,*,*,*,15,*,*,*;

%e *,*,*,*,*,20,*,*,*;

%e *,*,*,*,*,*,*,*,*,*;

%e *,9,*,*,*,*,*,32,*,*,*;

%e *,*,14,*,*,*,*,*,39,*,*,*; etc.

%e where * marks the non-integer values of (2*h*k + k + h - 3)/6 with h >= k >= 1. - _Vincenzo Librandi_, Jan 14 2013

%t Select[Range[0, 200], !PrimeQ[12 # + 7] &] (* _Vincenzo Librandi_, Jan 14 2013 *)

%o (Magma) [n: n in [0..150] | not IsPrime(12*n+7)]; // _Vincenzo Librandi_, Jan 14 2013

%Y Cf. A167056.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Oct 29 2009