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A153343 Numbers k such that 5*k + 4 is not prime.

%I A153343 #29 Sep 08 2022 08:45:39
%S A153343 0,1,2,4,6,7,8,9,10,12,13,14,16,18,19,20,22,23,24,25,26,28,30,31,32,
%T A153343 33,34,36,37,38,40,41,42,43,44,46,48,49,50,51,52,54,55,56,57,58,59,60,
%U A153343 61,62,63,64,65,66,67,68,70,72,73,74,76,78,79,80,82,84,85,86,88
%N A153343 Numbers k such that 5*k + 4 is not prime.
%C A153343 Apart from a(0) = 0 and a(1) = 1 this sequence comprises those numbers k such that (5*k)!/(5*k + 4) is an integer. - _Peter Bala_, Jan 25 2017
%H A153343 Vincenzo Librandi, <a href="/A153343/b153343.txt">Table of n, a(n) for n = 1..1000</a>
%e A153343 Distribution of the odd terms in the following triangular array:
%e A153343    1;
%e A153343    *,   *;
%e A153343    *,   *,   9;
%e A153343    *,   *,   *,   *;
%e A153343    *,   *,   *,  19,   *;
%e A153343    7,   *,   *,   *,   *,  33;
%e A153343    *,   *,   *,   *,   *,   *,   *;
%e A153343    *,   *,  23,   *,   *,   *,   *,  57;
%e A153343    *,   *,   *,   *,  41,   *,   *,   *,   *;
%e A153343    *,   *,   *,  37,   *,   *,   *,   *,  79,   *;
%e A153343   13,   *,   *,   *,   *,  59,   *,   *,   *,   *,  105;
%e A153343 etc., where * marks the noninteger values of (4*h*k + 2*k + 2*h - 3)/5 with h >= k >= 1. - _Vincenzo Librandi_, Jan 17 2013
%p A153343 # produces the sequence apart from the initial terms 0 and 1
%p A153343 for n from 0 to 100 do
%p A153343 if irem(factorial(5*n), 5*n+4) = 0 then print(n); end if;
%p A153343 end do: # _Peter Bala_, Jan 25 2017
%t A153343 Select[Range[0, 200], !PrimeQ[5*# + 4]&] (* _Vincenzo Librandi_, Jan 12 2013 *)
%o A153343 (Magma) [n: n in [0..150] | not IsPrime(5*n + 4)]; // _Vincenzo Librandi_, Jan 12 2013
%Y A153343 Cf. A024897, A014076, A153170, A045751, A095277, A153088, A153343.
%K A153343 nonn,easy
%O A153343 1,3
%A A153343 _Vincenzo Librandi_, Dec 24 2008
%E A153343 Erroneous comment deleted by _N. J. A. Sloane_, Jun 23 2010
%E A153343 0 added by _Arkadiusz Wesolowski_, Aug 03 2011