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 A153309 Numbers k such that 3*k + 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 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

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Last modified May 9 20:59 EDT 2021. Contains 343746 sequences. (Running on oeis4.)