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

0, 2, 5, 6, 8, 11, 12, 14, 16, 17, 19, 20, 21, 23, 26, 29, 30, 31, 32, 33, 35, 36, 38, 40, 41, 42, 44, 46, 47, 50, 51, 52, 53, 54, 55, 56, 59, 61, 62, 63, 65, 66, 68, 71, 72, 74, 75, 76, 77, 80, 81, 82, 83, 85, 86, 89, 90, 91, 92, 94, 95, 96, 98, 101, 103, 104, 106, 107, 109

Offset: 1

Author

Felice Russo

Keywords

• nonn
• easy

Comments

Terms (except 0) can be written as 4xy +- (x+y) for x > 0, y > 0. - Ron R Spencer, Jul 28 2016

Numbers k such that (4*k)!/(4*k + 1) is an integer. - Peter Bala, Jan 25 2017

Examples

			Distribution of the positive terms in the following triangular array:
   2;
   *,   6;
   5,   *,  12;
   *,  11,   *,  20;
   8,   *,  19,   *,  30;
   *,  16,   *,  29,   *,  42;
  11,   *,  26,   *,  41,   *,  56;
   *,  21,   *,  38,   *,  55,   *,  72;
  14,   *,  33,   *,  52,   *,  71,   *,  90;
   *,  26,   *,  47,   *,  68,   *,  89,   *, 110;
  17,   *,  40,   *,  63,   *,  86,   *, 109,   *, 132;
etc., where * marks the noninteger values of (2*h*k + k + h)/2 with h >= k >= 1. - _Vincenzo Librandi_, Jan 14 2013
		

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

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

Programs

Magma

[n: n in [0..220]| not IsPrime(4*n+1)]; // Vincenzo Librandi, Jan 28 2011

Maple

for n from 0 to 100 do
if irem(factorial(4*n), 4*n+1) = 0 then print(n); end if;
end do: # Peter Bala, Jan 25 2017

Mathematica

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

PARI

is(n)=!isprime(4*n+1) \\ Charles R Greathouse IV, Jul 29 2016

Extensions

More terms from Erich Friedman