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A155723 Numbers k such that 2*k + 9 is not prime.

%I A155723 #18 Sep 08 2022 08:45:41
%S A155723 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 A155723 45,48,51,53,54,55,56,57,58,60,62,63,66,67,68,69,72,73,75,76,78,80,81,
%U A155723 83,84,87,88,89,90,93,96,97,98,99,100,102,103,104,105,106,108,111,113,114
%N A155723 Numbers k such that 2*k + 9 is not prime.
%C A155723 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 A155723 Vincenzo Librandi, <a href="/A155723/b155723.txt">Table of n, a(n) for n = 1..10000</a>
%e A155723 Distribution of the terms in the following triangular array:
%e A155723    0;
%e A155723    3,  8;
%e A155723    6, 13, 20;
%e A155723    9, 18, 27,  36;
%e A155723   12, 23, 34,  45,  56;
%e A155723   15, 28, 41,  54,  67,  80;
%e A155723   18, 33, 48,  63,  78,  93, 108;
%e A155723   21, 38, 55,  72,  89, 106, 123, 140;
%e A155723   24, 43, 62,  81, 100, 119, 138, 157, 176;
%e A155723   27, 48, 69,  90, 111, 132, 153, 174, 195, 216;
%e A155723   30, 53, 76,  99, 122, 145, 168, 191, 214, 237, 260;
%e A155723   33, 58, 83, 108, 133, 158, 183, 208, 233, 258, 283, 308;
%e A155723   36, 63, 90, 117, 144, 171, 198, 225, 252, 279, 306, 333, 360;
%e A155723   etc.
%e A155723 the values of (2*h*k + k + h - 4) with h >= k >= 1. - _Vincenzo Librandi_, Jan 16 2013
%t A155723 Select[Range[0,80],!PrimeQ[2*#+9]&] (* _Vincenzo Librandi_, Mar 01 2012 *)
%o A155723 (Magma) [n: n in [0..115]| not IsPrime(2*n+9)]; // _Vincenzo Librandi_, Mar 01 2012
%Y A155723 Cf. A155724, A155722.
%K A155723 nonn,easy
%O A155723 1,2
%A A155723 _Vincenzo Librandi_, Jan 25 2009