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Numbers n such that 13*n + 5 is not prime.
1

%I #13 Sep 08 2022 08:45:41

%S 1,3,4,5,7,9,10,11,12,13,14,15,16,17,19,20,21,22,23,25,26,27,28,29,30,

%T 31,33,34,35,36,37,39,40,41,42,43,45,46,47,48,49,50,51,52,53,54,55,57,

%U 58,59,60,61,63,64,65,67,68,69,70,71,73,75,76,77,79,80,81

%N Numbers n such that 13*n + 5 is not prime.

%H Vincenzo Librandi, <a href="/A155935/b155935.txt">Table of n, a(n) for n = 1..1000</a>

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

%e *;

%e *,*;

%e *,*,*;

%e *,*,*,*;

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

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

%e *,*,*,10,*,*,*;

%e *,*,*,*,14,*,*,*;

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

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

%e *,*,12,*,*,*,*,*,*,*,*;

%e *,*,*,*,*,*,*,*,*,40,*,*; etc.

%e where * marks the non-integer values of (4*h*k + 2*k + 2*h - 4)/13 with h >= k >= 1. - _Vincenzo Librandi_, Jan 15 2013

%t Select[Range[0, 100], !PrimeQ[13 # + 5] &] (* _Vincenzo Librandi_, Oct 15 2012 *)

%o (Magma) [n: n in [0..90] | not IsPrime(13*n + 5)];

%Y Cf. A102732, A154610.

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Jan 31 2009