A348062 Primes p such that the length of the (eventual) period of the sequence {2^(2^k) mod p: k >= 0} is odd.

2, 3, 5, 17, 29, 43, 47, 113, 127, 179, 197, 257, 277, 283, 293, 317, 383, 439, 449, 467, 479, 509, 569, 641, 659, 719, 797, 863, 1013, 1069, 1289, 1373, 1399, 1427, 1439, 1487, 1579, 1627, 1657, 1753, 1823, 1913, 1933, 1949, 2063, 2203, 2207, 2213, 2273, 2339, 2351

Offset

1,1

Comments

Of these numbers only 3 and 5 are elite primes (A102742). (Aigner)

Every prime of the form A036259(n)*2^m + 1, with m, n >= 1, is in this sequence.

Links

Table of n, a(n) for n=1..51.

Alexander Aigner, Über Primzahlen, nach denen (fast) alle Fermatzahlen quadratische Nichtreste sind, Monatsh. Math., Vol. 101 (1986), pp. 85-93; alternative link.

Prog

(PARI) L=List([2]); forprime(p=3, 2351, z=znorder(Mod(2, p)); if(znorder(Mod(2, z/2^valuation(z, 2)))%2, listput(L, p))); Vec(L)

Crossrefs

Supersequence of A023394.

Cf. A102742 (elite primes), A256607.

Sequence in context: A127062 A214735 A216061 * A349678 A029972 A077498

Adjacent sequences: A348059 A348060 A348061 * A348063 A348064 A348065

Keyword

nonn

Author

Arkadiusz Wesolowski, Sep 26 2021

Status

approved