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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
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
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
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