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A153329 Numbers k such that 5*k + 1 is not prime.

%I A153329 #26 Sep 08 2022 08:45:39
%S A153329 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 A153329 33,34,35,37,39,40,41,43,44,45,46,47,49,51,52,53,55,57,58,59,60,61,63,
%U A153329 64,65,67,68,69,70,71,72,73,74,75,76,77,78,79,81,82,83,85,87
%N A153329 Numbers k such that 5*k + 1 is not prime.
%C A153329 Numbers k such that (5*k)!/(5*k + 1) is an integer. - _Peter Bala_, Jan 25 2017
%H A153329 Vincenzo Librandi, <a href="/A153329/b153329.txt">Table of n, a(n) for n = 1..1000</a>
%e A153329 Distribution of the even terms in the following triangular array:
%e A153329    *;
%e A153329    *,  *;
%e A153329    4,  *,  *;
%e A153329    *,  *,  *, 16;
%e A153329    *,  *,  *,  *, 24;
%e A153329    *,  *, 18,  *,  *,  *;
%e A153329    *,  *,  *,  *,  *,  *,  *;
%e A153329   10,  *,  *,  *,  *, 44,  *,  *;
%e A153329    *,  *,  *, 34,  *,  *,  *,  *, 72;
%e A153329    *,  *,  *,  *, 46,  *,  *,  *,  *, 88;
%e A153329    *,  *, 32,  *,  *,  *,  *, 78,  *,  *,  *;
%e A153329 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 A153329 for n from 0 to 100 do
%p A153329 if irem(factorial(5*n), 5*n+1) = 0 then print(n); end if;
%p A153329 end do: # _Peter Bala_, Jan 25 2017
%t A153329 Select[Range[0, 200], !PrimeQ[5*# + 1]&] (* _Vincenzo Librandi_, Jan 12 2013 *)
%o A153329 (Magma) [n: n in [0..150] | not IsPrime(5*n + 1)]; // _Vincenzo Librandi_, Jan 12 2013
%Y A153329 Cf. A024894, A014076, A153170, A045751, A095277, A153088, A153343.
%K A153329 nonn,easy
%O A153329 1,3
%A A153329 _Vincenzo Librandi_, Dec 23 2008
%E A153329 Erroneous comment deleted by _N. J. A. Sloane_, Jun 23 2010
%E A153329 0 added by _Arkadiusz Wesolowski_, Aug 03 2011