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A129493
Composite numbers k such that 3^k mod k is a power of 3.
6
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
1,1
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, ....
LINKS
EXAMPLE
14 is a member of the sequence since 3^14 mod 14 = 9.
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, #, # ]] &]
PROG
(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
KEYWORD
easy,nonn
AUTHOR
Robert G. Wilson v, Apr 17 2007
STATUS
approved