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

1,3

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

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

Sequence in context: A062958 A295075 A184996 * A047486 A229838 A191257

Adjacent sequences: A153306 A153307 A153308 * A153310 A153311 A153312

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