

A129492


Composite numbers k such that 2^k mod k is a power of 2.


6



6, 9, 10, 12, 14, 15, 20, 21, 22, 24, 26, 28, 30, 33, 34, 38, 39, 40, 44, 46, 48, 51, 52, 56, 57, 58, 60, 62, 63, 65, 66, 68, 69, 72, 74, 76, 78, 80, 82, 84, 85, 86, 87, 90, 92, 93, 94, 96, 102, 106, 111, 112, 114, 116, 118, 120, 122, 123, 124, 126, 129, 132, 133, 134, 138
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OFFSET

1,1


COMMENTS

Complement to composite numbers: 4, 8, 16, 18, 25, 27, 32, 35, 36, 42, 45, 49, 50, 54, 55, 64, 70, 75, 77, 81, 88, 91, 95, 98, 99, ....


LINKS



EXAMPLE

15 is a term since 2^15 mod 15 = 8.


MAPLE

filter:= proc(n) local k;
if isprime(n) then return false fi;
k:= 2 &^ n mod n;
k > 1 and k = 2^padic:ordp(k, 2)
end proc:


MATHEMATICA

Select[Range@ 141, IntegerQ@ Log[2, PowerMod[2, #, # ]] &]


PROG

(Magma) [k:k in [2..150] not IsPrime(k) and not IsZero(a) and (PrimeDivisors(a) eq [2]) where a is 2^k mod k ]; // Marius A. Burtea, Dec 04 2019


CROSSREFS



KEYWORD

easy,nonn


AUTHOR



STATUS

approved



