A396044 a(n) is the least k >= 1 such that A393641(n) is the greatest prime factor of 2^k + 1.

0, 1, 2, 5, 6, 4, 9, 10, 7, 18, 14, 12, 8, 15, 24, 11, 30, 26, 22, 13, 25, 21, 42, 33, 78, 34, 46, 36, 17, 20, 16, 35, 27, 19, 50, 54, 62, 38, 105

Offset

1,3

Comments

a(n) is the index of the first appearance of A393641(n) in A002587.

Links

Table of n, a(n) for n=1..39.

Formula

A002587(a(n)) = A393641(n).

a(n) = A002326((A393641(n)-1)/2) for n >= 2.

Example

a(4) = 5 because the greatest prime factor of 2^5 + 1 = 33 = 3 * 11 is 11 = A393641(4), and this is the first appearance of 11 in A002587.

Maple

A:= 0: count:= 1: P:= {}: p:= 2:
while count < 37 do
  p:= nextprime(p);
  m:= NumberTheory:-MultiplicativeOrder(2, p);
  if m::odd then next fi;
  m:= m/2;
  t:= 2^m+1;
  t:= t/p^padic:-ordp(t, p);
  for q in P do if t mod q = 0 then
    t:= t/q^padic:-ordp(t, q);
    if t = 1 then break fi;
  fi od;
  if t = 1 then count:= count+1; A:= A, m; fi;
  P:= P union {p};
od:
A;

Crossrefs

Cf. A002326, A002587, A393641, A396043.

Sequence in context: A343933 A262152 A016636 * A103989 A397373 A239049

Adjacent sequences: A396041 A396042 A396043 * A396045 A396046 A396047

Keyword

nonn,more

Author

Robert Israel, May 14 2026

Status

approved