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

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, 33, 34, 36, 37, 38, 40, 41, 42, 43, 44, 46, 48, 49, 50, 51, 52, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 70, 72, 73, 74, 76, 78, 79, 80, 82, 84, 85, 86, 88

Offset

1,3

Comments

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

Links

Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Example

Distribution of the odd terms in the following triangular array:
   1;
   *,   *;
   *,   *,   9;
   *,   *,   *,   *;
   *,   *,   *,  19,   *;
   7,   *,   *,   *,   *,  33;
   *,   *,   *,   *,   *,   *,   *;
   *,   *,  23,   *,   *,   *,   *,  57;
   *,   *,   *,   *,  41,   *,   *,   *,   *;
   *,   *,   *,  37,   *,   *,   *,   *,  79,   *;
  13,   *,   *,   *,   *,  59,   *,   *,   *,   *,  105;
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

Maple

# produces the sequence apart from the initial terms 0 and 1
for n from 0 to 100 do
if irem(factorial(5*n), 5*n+4) = 0 then print(n); end if;
end do: # Peter Bala, Jan 25 2017

Mathematica

Select[Range[0, 200], !PrimeQ[5*# + 4]&] (* Vincenzo Librandi, Jan 12 2013 *)

Prog

(Magma) [n: n in [0..150] | not IsPrime(5*n + 4)]; // Vincenzo Librandi, Jan 12 2013

Crossrefs

Cf. A024897, A014076, A153170, A045751, A095277, A153088, A153343.

Sequence in context: A155939 A114145 A153351 * A136499 A047513 A039068

Adjacent sequences: A153340 A153341 A153342 * A153344 A153345 A153346

Keyword

nonn,easy

Author

Vincenzo Librandi, Dec 24 2008

Extensions

Erroneous comment deleted by N. J. A. Sloane, Jun 23 2010

0 added by Arkadiusz Wesolowski, Aug 03 2011

Status

approved