A397249 - OEIS

A397249

Numbers m such that lambda(2^m - 1) + 1 is prime, where the Carmichael lambda function is A002322.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 31, 32, 34, 37, 38, 39, 40, 45, 48, 49, 50, 51, 52, 54, 56, 57, 61, 62, 65, 66, 68, 72, 77, 81, 83, 85, 87, 89, 107, 122, 127, 131, 133, 138, 179, 182, 219, 234, 235, 254, 310, 350, 376, 429, 456, 521, 534

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Numbers m such that A387107(m) + 1 is prime. Are there infinitely many such m?

It contains, among others, all Mersenne primes (A000668) and all Fermat primes (A019434).

In the above sequence, some prime repeat in pairs. Are there only finitely many such doubles?

LINKS

Amiram Eldar, Table of n, a(n) for n = 1..81

MATHEMATICA

q[m_] := PrimeQ[CarmichaelLambda[2^m-1] + 1]; Select[Range[100], q] (* Amiram Eldar, Aug 21 2026 *)

CROSSREFS

Cf. A000043 (subsequence), A000225, A000668, A002322 (lambda), A019434, A092506, A387107 (lambda(2^n-1)).

Sequence in context: A338265 A110303 A347520 * A180493 A346132 A320249

Adjacent sequences: A397245 A397247 A397248 * A397250 A397251 A397252

KEYWORD

nonn,new

AUTHOR

Thomas Ordowski, Aug 21 2026

EXTENSIONS

More terms from Daniel Suteu via SeqFan, Aug 12 2026

STATUS

approved