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A045751 Numbers k such that 4*k + 1 is not prime.

%I A045751 #51 Sep 08 2022 08:44:56
%S A045751 0,2,5,6,8,11,12,14,16,17,19,20,21,23,26,29,30,31,32,33,35,36,38,40,
%T A045751 41,42,44,46,47,50,51,52,53,54,55,56,59,61,62,63,65,66,68,71,72,74,75,
%U A045751 76,77,80,81,82,83,85,86,89,90,91,92,94,95,96,98,101,103,104,106,107,109
%N A045751 Numbers k such that 4*k + 1 is not prime.
%C A045751 Terms (except 0) can be written as 4xy +- (x+y) for x > 0, y > 0. - _Ron R Spencer_, Jul 28 2016
%C A045751 Numbers k such that (4*k)!/(4*k + 1) is an integer. - _Peter Bala_, Jan 25 2017
%H A045751 Vincenzo Librandi, <a href="/A045751/b045751.txt">Table of n, a(n) for n = 1..1000</a>
%e A045751 Distribution of the positive terms in the following triangular array:
%e A045751    2;
%e A045751    *,   6;
%e A045751    5,   *,  12;
%e A045751    *,  11,   *,  20;
%e A045751    8,   *,  19,   *,  30;
%e A045751    *,  16,   *,  29,   *,  42;
%e A045751   11,   *,  26,   *,  41,   *,  56;
%e A045751    *,  21,   *,  38,   *,  55,   *,  72;
%e A045751   14,   *,  33,   *,  52,   *,  71,   *,  90;
%e A045751    *,  26,   *,  47,   *,  68,   *,  89,   *, 110;
%e A045751   17,   *,  40,   *,  63,   *,  86,   *, 109,   *, 132;
%e A045751 etc., where * marks the noninteger values of (2*h*k + k + h)/2 with h >= k >= 1. - _Vincenzo Librandi_, Jan 14 2013
%p A045751 for n from 0 to 100 do
%p A045751 if irem(factorial(4*n), 4*n+1) = 0 then print(n); end if;
%p A045751 end do: # _Peter Bala_, Jan 25 2017
%t A045751 Select[Range[0, 200], ! PrimeQ[4 # + 1] &]
%o A045751 (Magma) [n: n in [0..220]| not IsPrime(4*n+1)]; // _Vincenzo Librandi_, Jan 28 2011
%o A045751 (PARI) is(n)=!isprime(4*n+1) \\ _Charles R Greathouse IV_, Jul 29 2016
%Y A045751 Cf. A014076, A153170, A095277, A153088, A153329, A153343.
%K A045751 nonn,easy
%O A045751 1,2
%A A045751 _Felice Russo_
%E A045751 More terms from _Erich Friedman_