A140797 -id:A140797 - cp's OEIS frontend

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

Vladimir Shevelev, Aug 24 2008

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

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.

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

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

A297625 Primes of the form (2^(p^k) - 1)/(2^(p^(k - 1)) - 1), with p prime and k > 1.

Original entry on oeis.org

5, 17, 73, 257, 65537, 262657, 4432676798593

Offset: 1

Arkadiusz Wesolowski, Jan 04 2018

nonn

Primes of the form Phi(x, 2), where x is a proper prime power and Phi is the cyclotomic polynomial.
Together with 3, supersequence of A019434.
Also called Mersenne-Fermat primes.
a(8) has 1031 digits and is too large to include.

Fredrick Kennard, Unsolved Problems in Mathematics, Lulu Press, 2015, p. 160.

Wikipedia, Mersenne-Fermat primes

Cf. A019434, A051156, A140797, A187823, A245730, A246547.

lst:=[]; r:=7; pr:=PrimesUpTo(r); for k in [2..r] do for c in [1..#pr] do p:=pr[c]; if p^k le r^2 then MF:=Truncate((2^(p^k)-1)/(2^(p^(k-1))-1)); if IsPrime(MF) then Append(~lst, MF); end if; end if; end for; end for; Sort(lst);

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Links

Crossrefs

Extensions