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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
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
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
KEYWORD
nonn,easy
AUTHOR
EXTENSIONS
More terms from Erich Friedman
STATUS
approved