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A153170 Numbers k such that 3*k + 2 is not prime.

%I A153170 #31 Sep 08 2022 08:45:39
%S A153170 2,4,6,8,10,11,12,14,16,18,20,21,22,24,25,26,28,30,31,32,34,36,38,39,
%T A153170 40,41,42,44,46,47,48,50,51,52,53,54,56,58,60,61,62,64,66,67,68,69,70,
%U A153170 71,72,73,74,76,78,80,81,82,84,86,88,90,91,92,94,95,96,98,99,100,101,102
%N A153170 Numbers k such that 3*k + 2 is not prime.
%C A153170 Contains the positive even numbers (A005843) and the odd numbers of the form 2*A059324(.) + 1. - _R. J. Mathar_, Nov 27 2010
%C A153170 Numbers k such that (3*k)!/(3*k + 2) is an integer. - _Peter Bala_, Jan 25 2017
%H A153170 Vincenzo Librandi, <a href="/A153170/b153170.txt">Table of n, a(n) for n = 1..1000</a>
%e A153170 Distribution of the odd terms in the following triangular array:
%e A153170   *;
%e A153170   *,   *;
%e A153170   *,  11,   *;
%e A153170   *,   *,   *,   *;
%e A153170   *,   *,  25,   *,   *;
%e A153170   *,  21,   *,   *,  47,   *;
%e A153170   *,   *,   *,   *,   *,   *,   *;
%e A153170   *,   *,  39,   *,   *,  73,   *,   *;
%e A153170   *,  31,   *,   *,  69,   *,   *, 107,   *;
%e A153170   *,   *,   *,   *,   *,   *,   *,   *,   *,   *;
%e A153170   *,   *,  53,   *,   *,  99,   *,   *, 145,   *,   *;
%e A153170   *,  41,   *,   *,  91,   *,   *, 141,   *,   *, 191,   *;
%e A153170 etc., where * marks the noninteger values of (4*h*k + 2*k + 2*h - 1)/3 with h >= k >= 1. - _Vincenzo Librandi_, Jan 15 2013
%p A153170 for n from 0 to 100 do
%p A153170 if irem(factorial(3*n), 3*n+2) = 0 then print(n); end if;
%p A153170 end do: # _Peter Bala_, Jan 25 2017
%t A153170 Select[Range[1, 200], !PrimeQ[3*# + 2] &] (* _Vincenzo Librandi_, Oct 11 2012 *)
%o A153170 (PARI) for(n=1,200,if(!isprime(3*n+2), print1(n,", "))) \\  _Joerg Arndt_, Nov 27 2010
%o A153170 (Magma) [n: n in [1..110] | not IsPrime(3*n + 2)]; // _Vincenzo Librandi_, Oct 11 2012
%Y A153170 Cf. A024893, A014076, A045751, A095277, A153088, A153329, A153343.
%K A153170 nonn,easy
%O A153170 1,1
%A A153170 _Vincenzo Librandi_, Dec 20 2008
%E A153170 Edited by _N. J. A. Sloane_, Jun 23 2010