A049593 Primes p for which residue of ((p-1)! + 1) modulo (p + 16) equals 1.

11, 17, 19, 23, 29, 41, 47, 53, 59, 61, 71, 79, 83, 89, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 167, 173, 179, 191, 193, 197, 199, 227, 229, 233, 239, 251, 257, 263, 269, 271, 281, 283, 293, 307, 311, 313, 317, 347, 349, 353, 359, 379, 383, 389, 397

Offset

1,1

Comments

Primes p such that p+16 divides (p-1)!. - Robert Israel, Aug 30 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

11 is in the sequence because 10! + 1 = 3628801 has the form (11+16)k + 1 = 27k + 1 = 27*134400 + 1.

Maple

filter:= proc(p) local L, t, q, s, i, r;
  if not isprime(p) then return false fi;
  for s in ifactors(p+16)[2] do
    t:= 0: q:= s[1];
    for i from 1 do
      r:= floor((p-1)/q^i);
      if r = 0 then return false fi;
      t:= t+r;
      if t >= s[2] then break fi;
    od;
  od;
  true
end proc:
select(filter, [seq(i, i=3..1000, 2)]); # Robert Israel, Aug 30 2018

Mathematica

Reap[For[p = 2, p < 1000, p = NextPrime[p], If[Divisible[(p - 1)!, p + 16], Sow[p]]]][[2, 1]] (* Jean-François Alcover, Jun 09 2020 *)

Prog

(PARI) isok(p) = isprime(p) && (Mod((p-1), (p+16)) == 0); \\ Michel Marcus, Jun 09 2020

Crossrefs

Sequence in context: A038966 A050778 A316100 * A216664 A019412 A178641

Adjacent sequences: A049590 A049591 A049592 * A049594 A049595 A049596

Keyword

nonn

Author

Labos Elemer

Status

approved