A141629 a(n) is the least base-2 overpseudoprime k such that the multiplicative order of 2 mod k equals 8*n+20.

3277, 4033, 838861, 8321, 80581, 130561, 104653, 20647621, 280601, 818201, 68719214593, 57646075230342349, 48448661, 1353244757701, 351479006145541, 88357, 390937, 1846171781, 17585969, 9774181, 28147501026509, 3882413703281, 1251949, 9007199388958721

Offset: 1

Author

Vladimir Shevelev, Aug 24 2008

Keywords

• nonn
• more

Comments

C. Pomerance proved (private correspondence) that for every n>=1 there exists at least one overpseudoprime (a(n)) for which the multiplicative order of 2 mod a(n) equals 8n+20.

a(25) > 2^64. - Amiram Eldar, Nov 09 2023

Links

• Amiram Eldar, Table of n, a(n) for n = 1..1000, with zeros for 277 unknown values that are > 2^64.
• Vladimir Shevelev, An upper estimate for the overpseudoprime counting function, arXiv:0807.1975 [math.NT], 2008.

Crossrefs

Cf. A141232, A122929, A140452, A140797, A140803.

Extensions

a(4) corrected and a(12)-a(24) added by Amiram Eldar, Nov 09 2023