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

%I #37 Sep 08 2022 08:45:39

%S 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,

%T 38,39,40,41,43,44,45,47,48,49,51,53,55,56,57,58,59,61,62,63,65,67,68,

%U 69,71,72,73,75,77,78,79,81,82,83,84,85,86,87,88,89,91,93,95

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

%C Terms (except 0) can be written as 3xy +- (x + y) for x > 0, y > 0. - _Ron R Spencer_, Aug 01 2016

%C 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

%H Vincenzo Librandi, <a href="/A153309/b153309.txt">Table of n, a(n) for n = 1..1000</a>

%e Distribution of the even terms in the following triangular array:

%e *;

%e * 8;

%e * * 16;

%e * * * *;

%e * 18 * * 40;

%e * * 30 * * 56;

%e * * * * * * *;

%e * 28 * * 62 * * 96;

%e * * 44 * * 82 * * 120;

%e * * * * * * * * * *;

%e * 38 * * 84 * * 130 * * 176;

%e * * 58 * * 108 * * 158 * * 208;

%e etc., where * marks the noninteger values of (4*h*k + 2*k + 2*h)/3 with h >= k >= 1. - _Vincenzo Librandi_, Jan 17 2013

%p # produces the sequence apart from the term equal to 1

%p for n from 0 to 100 do

%p if irem(factorial(3*n), 3*n+1) = 0 then print(n); end if;

%p end do: # _Peter Bala_, Jan 25 2017

%t Select[Range[0, 200], !PrimeQ[3*# + 1]&] (* _Vincenzo Librandi_, Jan 12 2013 *)

%o (Magma) [n: n in [0..150] | not IsPrime(3*n + 1)]; // _Vincenzo Librandi_, Jan 12 2013

%o (PARI) is(n)=!isprime(3*n+1) \\ _Charles R Greathouse IV_, Aug 01 2016

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

%K nonn,easy

%O 1,3

%A _Vincenzo Librandi_, Dec 23 2008

%E Erroneous comment deleted by _N. J. A. Sloane_, Jun 23 2010

%E 0 added by _Arkadiusz Wesolowski_, Jun 25 2011

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Last modified April 16 14:51 EDT 2024. Contains 371749 sequences. (Running on oeis4.)