

A045751


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


14



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
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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



