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