A129494 Composite numbers k such that 4^k mod k is a power of 4 greater than 1.

6, 12, 15, 20, 22, 24, 26, 28, 30, 34, 38, 40, 46, 48, 56, 58, 60, 62, 66, 69, 72, 74, 77, 80, 82, 84, 85, 86, 87, 88, 91, 93, 94, 96, 102, 104, 105, 106, 111, 117, 118, 120, 122, 123, 126, 129, 132, 134, 140, 141, 142, 144, 146, 158, 159, 166, 168, 170, 177, 178, 182

Offset: 1

Author

Robert G. Wilson v, Apr 17 2007

Keywords

• easy
• nonn

Comments

Complement to composite numbers: 4, 8, 9, 10, 14, 16, 18, 21, 25, 27, 32, 33, 35, 36, 39, 42, 44, 45, 49, 50, 51, 52, 54, 55, 57, ... - R. J. Mathar, May 16 2008

Examples

			22 is a term since 4^22 mod 22 = 16.
		

Links

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

Crossrefs

Cf. A036236, A129492, A129493, A129495, A129496, A129497.

Contains A122781 except for 1 and 4.

Programs

Magma

[k:k in [2..200]| not IsPrime(k)  and  not IsZero(a)  and (PrimeDivisors(a) eq [2]) and  &+[j[1]*j[2]: j in Factorization(a) ] mod 4 eq 0 where a is 4^k mod k]; // Marius A. Burtea, Dec 04 2019

Maple

filter:= proc(n) local k,j;
  if isprime(n) then return false fi;
  k:= 4 &^ n mod n;
  j:= padic:-ordp(k,2);
  k>1 and j::even and k = 2^j
end proc:
select(filter, [$4..1000]); # Robert Israel, Dec 03 2019

Mathematica

Select[ Range@ 161, IntegerQ@ Log[4, PowerMod[4, #, # ]] &]

Extensions

Corrected and extended by R. J. Mathar, May 16 2008