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

1,1

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

Links

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

Example

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

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, #, # ]] &]

Prog

(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

Crossrefs

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

Contains A122781 except for 1 and 4.

Sequence in context: A315617 A287572 A315618 * A001284 A320142 A063931

Adjacent sequences: A129491 A129492 A129493 * A129495 A129496 A129497

Keyword

easy,nonn

Author

Robert G. Wilson v, Apr 17 2007

Extensions

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

Status

approved