A095277 Numbers k such that 4k + 3 is composite.

3, 6, 8, 9, 12, 13, 15, 18, 21, 22, 23, 24, 27, 28, 29, 30, 33, 35, 36, 38, 39, 42, 43, 45, 46, 48, 50, 51, 53, 54, 57, 58, 60, 61, 63, 64, 66, 68, 69, 71, 72, 73, 74, 75, 78, 79, 80, 81, 83, 84, 85, 87, 88, 90, 92, 93, 96, 97, 98, 99, 100, 101, 102, 103, 105, 106, 108

Offset

1,1

Comments

Terms can be written as (4xy +- (x-y)) - 1 for x > 0, y > 0. - Ron R Spencer, Aug 01 2016

Numbers k such that (4*k)!/(4*k + 3) is an integer. - Peter Bala, Jan 25 2017

Links

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

Formula

a(n) = (A091236(n) - 3)/4.

Example

Distribution of the positive terms in the following triangular array:
  *;
  3,  *;
  *,  8,  *;
  6,  *, 15,  *;
  *, 13,  *, 24,  *;
  9,  *, 22,  *, 35,  *;
  *, 18,  *, 33,  *, 48,  *;
etc., where * marks the noninteger values of (2*h*k + k + h-1)/2 with h >= k >= 1. - Vincenzo Librandi, Apr 22 2014

Maple

for n from 0 to 100 do
if irem(factorial(4*n), 4*n+3) = 0 then print(n); end if;
end do: # Peter Bala, Jan 25 2017

Mathematica

Select[Range[150], !PrimeQ[4#+3]&] (* Harvey P. Dale, Jul 04 2011 *)

Prog

(Magma) [n: n in [0..110] |not IsPrime(4*n+3)]; // Vincenzo Librandi, Apr 22 2014\
(PARI) is(n)=!isprime(4*n+3) \\ Charles R Greathouse IV, Aug 01 2016

Crossrefs

Complement of A095278. Cf. also A045751, A014076, A153170, A153088, A153329, A153343.

Sequence in context: A275608 A363758 A155723 * A185717 A189637 A182338

Adjacent sequences: A095274 A095275 A095276 * A095278 A095279 A095280

Keyword

nonn,easy

Author

Antti Karttunen, Jun 01 2004

Status

approved