OFFSET
1,3
COMMENTS
Terms (except 0) can be written as 3xy +- (x + y) for x > 0, y > 0. - Ron R Spencer, Aug 01 2016
Apart from a(2) = 1 the sequence comprises those numbers k such that (3*k)!/(3*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 even terms in the following triangular array:
*;
* 8;
* * 16;
* * * *;
* 18 * * 40;
* * 30 * * 56;
* * * * * * *;
* 28 * * 62 * * 96;
* * 44 * * 82 * * 120;
* * * * * * * * * *;
* 38 * * 84 * * 130 * * 176;
* * 58 * * 108 * * 158 * * 208;
etc., where * marks the noninteger values of (4*h*k + 2*k + 2*h)/3 with h >= k >= 1. - Vincenzo Librandi, Jan 17 2013
MAPLE
# produces the sequence apart from the term equal to 1
for n from 0 to 100 do
if irem(factorial(3*n), 3*n+1) = 0 then print(n); end if;
end do: # Peter Bala, Jan 25 2017
MATHEMATICA
Select[Range[0, 200], !PrimeQ[3*# + 1]&] (* Vincenzo Librandi, Jan 12 2013 *)
PROG
(Magma) [n: n in [0..150] | not IsPrime(3*n + 1)]; // Vincenzo Librandi, Jan 12 2013
(PARI) is(n)=!isprime(3*n+1) \\ Charles R Greathouse IV, Aug 01 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Vincenzo Librandi, Dec 23 2008
EXTENSIONS
Erroneous comment deleted by N. J. A. Sloane, Jun 23 2010
0 added by Arkadiusz Wesolowski, Jun 25 2011
STATUS
approved