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Numbers k such that 2*k + 9 is not prime.
4

%I #18 Sep 08 2022 08:45:41

%S 0,3,6,8,9,12,13,15,18,20,21,23,24,27,28,30,33,34,36,38,39,41,42,43,

%T 45,48,51,53,54,55,56,57,58,60,62,63,66,67,68,69,72,73,75,76,78,80,81,

%U 83,84,87,88,89,90,93,96,97,98,99,100,102,103,104,105,106,108,111,113,114

%N Numbers k such that 2*k + 9 is not prime.

%C 2*A155724(m,n) + 9 = (2n+1)*(2m+1) are not prime and create entries of this form. Also, one less than the associate entry in A153053, two less than the associated A153052. - _R. J. Mathar_, Jan 05 2011

%H Vincenzo Librandi, <a href="/A155723/b155723.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 0;

%e 3, 8;

%e 6, 13, 20;

%e 9, 18, 27, 36;

%e 12, 23, 34, 45, 56;

%e 15, 28, 41, 54, 67, 80;

%e 18, 33, 48, 63, 78, 93, 108;

%e 21, 38, 55, 72, 89, 106, 123, 140;

%e 24, 43, 62, 81, 100, 119, 138, 157, 176;

%e 27, 48, 69, 90, 111, 132, 153, 174, 195, 216;

%e 30, 53, 76, 99, 122, 145, 168, 191, 214, 237, 260;

%e 33, 58, 83, 108, 133, 158, 183, 208, 233, 258, 283, 308;

%e 36, 63, 90, 117, 144, 171, 198, 225, 252, 279, 306, 333, 360;

%e etc.

%e the values of (2*h*k + k + h - 4) with h >= k >= 1. - _Vincenzo Librandi_, Jan 16 2013

%t Select[Range[0,80],!PrimeQ[2*#+9]&] (* _Vincenzo Librandi_, Mar 01 2012 *)

%o (Magma) [n: n in [0..115]| not IsPrime(2*n+9)]; // _Vincenzo Librandi_, Mar 01 2012

%Y Cf. A155724, A155722.

%K nonn,easy

%O 1,2

%A _Vincenzo Librandi_, Jan 25 2009