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A049593 Primes p for which residue of ((p-1)! + 1) modulo (p + 16) equals 1. 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Primes p such that p+16 divides (p-1)!. - Robert Israel, Aug 30 2018
LINKS
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
KEYWORD
nonn
AUTHOR
STATUS
approved

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Last modified July 24 18:03 EDT 2024. Contains 374585 sequences. (Running on oeis4.)