A140803 -id:A140803 - 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

A246758 Prime numbers of the form (2^(mn)-1)/((2^m-1)(2^n-1)).

Original entry on oeis.org

3, 11, 43, 151, 683, 2731, 43691, 174763, 599479, 2796203, 715827883, 2932031007403, 10052678938039, 145295143558111, 581283643249112959, 658812288653553079, 768614336404564651, 9520972806333758431, 201487636602438195784363

Offset: 1

Nico Brown, Sep 02 2014

nonn

The sequence contains A000979 as a subsequence.

Both m and n must be prime.

			For m=3 and n=5, (2^15-1)/((2^3-1)(2^5-1))=151 is prime, so 151 is a member of the sequence.

Robert Israel, Table of n, a(n) for n = 1..39

Primes in A140803.

N:= 200: # to use all (p, q) with p*q < N
Primes:= select(isprime, [$2..floor(N/2)]):
A:= {}:
for i from 1 to nops(Primes) do
  p:= Primes[i];
  Qs:= select(q -> q < N/p, [seq(Primes[j], j=1..i-1)]);
  A:= A union {seq((2^(p*q)-1)/(2^p-1)/(2^q-1), q=Qs)};
od:
# in Maple 12 and up
select(isprime, A);
# or in earlier Maple versions
sort([select(isprime, , A); # _)[]])[];
# Robert Israel, Sep 02 2014

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.

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A246758 Prime numbers of the form (2^(mn)-1)/((2^m-1)(2^n-1)).

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Maple

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

A246758 Prime numbers of the form (2^(m*n)-1)/((2^m-1)*(2^n-1)).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

A246758 Prime numbers of the form (2^(mn)-1)/((2^m-1)(2^n-1)).