A396002 Primes p that are the least prime factor of 2^k + 1 for some k >= 1.

3, 5, 17, 97, 193, 257, 449, 641, 769, 2753, 3329, 4673, 5441, 5953, 6977, 7681, 7873, 7937, 10753, 11777, 12161, 12289, 13313, 14081, 14657, 15937, 18433, 19457, 26113, 28097, 29633, 35521, 36161, 36353, 36929, 37889, 40193, 40961, 42689, 44417, 45377, 45569, 46337, 47681, 48449, 51329, 51713

Offset

1,1

Comments

Numbers that occur in A002586.

Odd primes p such that A002326((p-1)/2) is even and there is no smaller odd prime q such that A002326((p-1)/2)/A002326((q-1)/2) is an odd integer.

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

a(4) = 97 is a term because 2^24 + 1 = 16777217 = 97 * 257 * 673 whose least prime factor is 97.

Maple

A:= NULL: V:= {}:
p:= 2:
while p < 10^6 do
  p:= nextprime(p); v:= NumberTheory:-MultiplicativeOrder(2, p)/2;
  if v::integer and andmap(w -> v mod w <> 0 or (v/w)::even, V) then
    A:= A, p; V:= V union {v}
  fi;
od:
A;

Crossrefs

Includes A019434. Cf. A002326, A002586, A395931, A393641.

Sequence in context: A100003 A283331 A114161 * A361180 A372867 A302199

Adjacent sequences: A395999 A396000 A396001 * A396004 A396005 A396006

Keyword

nonn

Author

Robert Israel, May 13 2026

Status

approved