OFFSET

1,2

COMMENTS

Numbers k such that the multiplicative order of 2 mod k is a power of 3.

If x and y are coprime members of the sequence, then x*y is in the sequence.

All divisors of a member of the sequence are in the sequence.

All prime-power divisors of 2^(3^k)-1 are in the sequence. In particular, the sequence contains infinitely many primes. - Robert Israel, Sep 02 2018

LINKS

Robert Israel, Table of n, a(n) for n = 1..82

EXAMPLE

a(3) = 73 is in the sequence because the multiplicative order of 2 mod 73 is 9 which is a power of 3.

MAPLE

N:= 10^6: # to get all terms <= N

Res:= NULL:

p:= 5:

do

p:= nextprime(p);

if p > N then break fi;

q:= 1: t:= 2:

while q < p-1 do

q:= 3*q;

t:= t^3 mod p;

if t = 1 then

Res:= Res, p;

v:= 1;

while 2 &^ t mod (p^(v+1)) = 1 do v:= v+1 od:

V[p]:= v;

break

fi

od

od:

S:= {1}:

for p in Res do

S:= `union`(S, seq(map(`*`, select(`<=`, S, N/p^i), p^i), i=1..V[p]))

od:

sort(convert(S, list));

CROSSREFS

KEYWORD

nonn

AUTHOR

Robert Israel, Aug 31 2018

STATUS

approved