A153329 - OEIS

%I #26 Sep 08 2022 08:45:39

%S 0,1,3,4,5,7,9,10,11,13,15,16,17,18,19,21,22,23,24,25,27,28,29,31,32,

%T 33,34,35,37,39,40,41,43,44,45,46,47,49,51,52,53,55,57,58,59,60,61,63,

%U 64,65,67,68,69,70,71,72,73,74,75,76,77,78,79,81,82,83,85,87

%N Numbers k such that 5*k + 1 is not prime.

%C Numbers k such that (5*k)!/(5*k + 1) is an integer. - _Peter Bala_, Jan 25 2017

%H Vincenzo Librandi, <a href="/A153329/b153329.txt">Table of n, a(n) for n = 1..1000</a>

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

%e    *;

%e    *,  *;

%e    4,  *,  *;

%e    *,  *,  *, 16;

%e    *,  *,  *,  *, 24;

%e    *,  *, 18,  *,  *,  *;

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

%e   10,  *,  *,  *,  *, 44,  *,  *;

%e    *,  *,  *, 34,  *,  *,  *,  *, 72;

%e    *,  *,  *,  *, 46,  *,  *,  *,  *, 88;

%e    *,  *, 32,  *,  *,  *,  *, 78,  *,  *,  *;

%e etc., where * marks the noninteger values of (4*h*k + 2*k + 2*h)/5 with h >= k >= 1. - _Vincenzo Librandi_, Jan 17 2013

%p for n from 0 to 100 do

%p if irem(factorial(5*n), 5*n+1) = 0 then print(n); end if;

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

%t Select[Range[0, 200], !PrimeQ[5*# + 1]&] (* _Vincenzo Librandi_, Jan 12 2013 *)

%o (Magma) [n: n in [0..150] | not IsPrime(5*n + 1)]; // _Vincenzo Librandi_, Jan 12 2013

%Y Cf. A024894, A014076, A153170, A045751, A095277, A153088, 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_, Aug 03 2011