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Numbers k such that 4*k + 1 is not prime.
14

%I #51 Sep 08 2022 08:44:56

%S 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 41,42,44,46,47,50,51,52,53,54,55,56,59,61,62,63,65,66,68,71,72,74,75,

%U 76,77,80,81,82,83,85,86,89,90,91,92,94,95,96,98,101,103,104,106,107,109

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

%C Terms (except 0) can be written as 4xy +- (x+y) for x > 0, y > 0. - _Ron R Spencer_, Jul 28 2016

%C Numbers k such that (4*k)!/(4*k + 1) is an integer. - _Peter Bala_, Jan 25 2017

%H Vincenzo Librandi, <a href="/A045751/b045751.txt">Table of n, a(n) for n = 1..1000</a>

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

%e 2;

%e *, 6;

%e 5, *, 12;

%e *, 11, *, 20;

%e 8, *, 19, *, 30;

%e *, 16, *, 29, *, 42;

%e 11, *, 26, *, 41, *, 56;

%e *, 21, *, 38, *, 55, *, 72;

%e 14, *, 33, *, 52, *, 71, *, 90;

%e *, 26, *, 47, *, 68, *, 89, *, 110;

%e 17, *, 40, *, 63, *, 86, *, 109, *, 132;

%e etc., where * marks the noninteger values of (2*h*k + k + h)/2 with h >= k >= 1. - _Vincenzo Librandi_, Jan 14 2013

%p for n from 0 to 100 do

%p if irem(factorial(4*n), 4*n+1) = 0 then print(n); end if;

%p end do: # _Peter Bala_, Jan 25 2017

%t Select[Range[0, 200], ! PrimeQ[4 # + 1] &]

%o (Magma) [n: n in [0..220]| not IsPrime(4*n+1)]; // _Vincenzo Librandi_, Jan 28 2011

%o (PARI) is(n)=!isprime(4*n+1) \\ _Charles R Greathouse IV_, Jul 29 2016

%Y Cf. A014076, A153170, A095277, A153088, A153329, A153343.

%K nonn,easy

%O 1,2

%A _Felice Russo_

%E More terms from _Erich Friedman_