A318688 Numbers k such that 2^(3^j) == 1 (mod k) for some j.

1, 7, 73, 487, 511, 2593, 3409, 18151, 35551, 39367, 71119, 80191, 97687, 189289, 209953, 248857, 262657, 275569, 379081, 472393, 497833, 561337, 683809, 1262791, 1299079, 1325023, 1469671, 1838599, 2653567, 2873791, 3306751, 5191687, 5853943, 7131151, 8839537, 9093553, 15326569, 19171729

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

Cf. A000244, A002326

Sequence in context: A076106 A202042 A294291 * A117982 A003535 A050917

Adjacent sequences: A318685 A318686 A318687 * A318689 A318690 A318691

Keyword

nonn

Author

Robert Israel, Aug 31 2018

Status

approved