cp's OEIS Frontend

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

%I A129494 #13 Aug 20 2023 17:01:25
%S A129494 6,12,15,20,22,24,26,28,30,34,38,40,46,48,56,58,60,62,66,69,72,74,77,
%T A129494 80,82,84,85,86,87,88,91,93,94,96,102,104,105,106,111,117,118,120,122,
%U A129494 123,126,129,132,134,140,141,142,144,146,158,159,166,168,170,177,178,182
%N A129494 Composite numbers k such that 4^k mod k is a power of 4 greater than 1.
%C A129494 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
%H A129494 Robert Israel, <a href="/A129494/b129494.txt">Table of n, a(n) for n = 1..10000</a>
%e A129494 22 is a term since 4^22 mod 22 = 16.
%p A129494 filter:= proc(n) local k,j;
%p A129494   if isprime(n) then return false fi;
%p A129494   k:= 4 &^ n mod n;
%p A129494   j:= padic:-ordp(k,2);
%p A129494   k>1 and j::even and k = 2^j
%p A129494 end proc:
%p A129494 select(filter, [$4..1000]); # _Robert Israel_, Dec 03 2019
%t A129494 Select[ Range@ 161, IntegerQ@ Log[4, PowerMod[4, #, # ]] &]
%o A129494 (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
%Y A129494 Cf. A036236, A129492, A129493, A129495, A129496, A129497.
%Y A129494 Contains A122781 except for 1 and 4.
%K A129494 easy,nonn
%O A129494 1,1
%A A129494 _Robert G. Wilson v_, Apr 17 2007
%E A129494 Corrected and extended by _R. J. Mathar_, May 16 2008