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

1,2

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

Links

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

Example

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

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] &]

Prog

(Magma) [n: n in [0..220]| not IsPrime(4*n+1)]; // Vincenzo Librandi, Jan 28 2011
(PARI) is(n)=!isprime(4*n+1) \\ Charles R Greathouse IV, Jul 29 2016

Crossrefs

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

Sequence in context: A024798 A108857 A132142 * A047267 A058591 A247062

Adjacent sequences: A045748 A045749 A045750 * A045752 A045753 A045754

Keyword

nonn,easy

Author

Felice Russo

Extensions

More terms from Erich Friedman

Status

approved