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A153309 Numbers n such that 3*n + 1 is not prime. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

COMMENTS

Numbers (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 n such that (3*n)!/(3*n + 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 non-integer 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

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Last modified November 19 11:04 EST 2017. Contains 294936 sequences.