A153309 Numbers k such that 3*k + 1 is not prime.

0, 1, 3, 5, 7, 8, 9, 11, 13, 15, 16, 17, 18, 19, 21, 23, 25, 27, 28, 29, 30, 31, 33, 35, 37, 38, 39, 40, 41, 43, 44, 45, 47, 48, 49, 51, 53, 55, 56, 57, 58, 59, 61, 62, 63, 65, 67, 68, 69, 71, 72, 73, 75, 77, 78, 79, 81, 82, 83, 84, 85, 86, 87, 88, 89, 91, 93, 95

Offset: 1

Author

Vincenzo Librandi, Dec 23 2008

Keywords

• nonn
• easy

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

Examples

			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
		

Links

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

Crossrefs

Cf. A024892, A014076, A153170, A045751, A095277, A153088, A153329, A153343.

Programs

Magma

[n: n in [0..150] | not IsPrime(3*n + 1)]; // Vincenzo Librandi, Jan 12 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 *)

PARI

is(n)=!isprime(3*n+1) \\ Charles R Greathouse IV, Aug 01 2016

Extensions

Erroneous comment deleted by N. J. A. Sloane, Jun 23 2010

0 added by Arkadiusz Wesolowski, Jun 25 2011