A129493 - OEIS

%I #14 Sep 08 2022 08:45:30

%S 6,10,12,14,18,22,24,26,30,33,34,36,38,39,46,51,54,56,57,58,62,63,66,

%T 69,72,74,78,82,86,87,90,91,92,93,94,99,104,106,108,111,112,116,117,

%U 118,120,121,122,123,124,129,132,134,135,141,142,144,146,148,154,158,159

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

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

%H Robert Israel, <a href="/A129493/b129493.txt">Table of n, a(n) for n = 1..10000</a>

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

%p filter:= proc(n) local k;

%p   if isprime(n) then return false fi;

%p   k:= 3 &^ n mod n;

%p   k > 1 and k = 3^padic:-ordp(k,3)

%p end proc:

%p select(filter, [$4..1000]); # _Robert Israel_, Dec 03 2019

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

%o (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

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

%K easy,nonn

%O 1,1

%A _Robert G. Wilson v_, Apr 17 2007