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A318688 Numbers k such that 2^(3^j) == 1 (mod k) for some j. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 1 01:37 EST 2021. Contains 349426 sequences. (Running on oeis4.)