A129493 Composite numbers k such that 3^k mod k is a power of 3.

6, 10, 12, 14, 18, 22, 24, 26, 30, 33, 34, 36, 38, 39, 46, 51, 54, 56, 57, 58, 62, 63, 66, 69, 72, 74, 78, 82, 86, 87, 90, 91, 92, 93, 94, 99, 104, 106, 108, 111, 112, 116, 117, 118, 120, 121, 122, 123, 124, 129, 132, 134, 135, 141, 142, 144, 146, 148, 154, 158, 159

Offset: 1

Author

Robert G. Wilson v, Apr 17 2007

Keywords

• easy
• nonn

Comments

Complement to composite numbers: 9, 15, 21, 25, 27, 28, 35, 42, 44, 45, 48, 49, 50, 52, 55, 60, 65, 68, 70, 75, ....

Examples

			14 is a member of the sequence since 3^14 mod 14 = 9.
		

Links

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

Crossrefs

Cf. A036236, A122780, A129492, A129494, A129495, A129496, A129497.

Programs

Magma

[k:k in [2..160]| not IsPrime(k)  and  not IsZero(a)  and (PrimeDivisors(a) eq [3]) where a is 3^k mod k ]; // Marius A. Burtea, Dec 04 2019

Maple

filter:= proc(n) local k;
  if isprime(n) then return false fi;
  k:= 3 &^ n mod n;
  k > 1 and k = 3^padic:-ordp(k,3)
end proc:
select(filter, [$4..1000]); # Robert Israel, Dec 03 2019

Mathematica

Select[Range@ 161, IntegerQ@ Log[3, PowerMod[3, #, # ]] &]