A079363 -id:A079363 - cp's OEIS frontend

A319535 Primes of the form 2*6^k - 1.

11, 71, 431, 2591, 15551, 4353564671, 5642219814911, 341163456359156416511, 2046980738154938499071, 20628849596981071092343898111, 26734989077687468135677691953151, 207891275068097752223029732627709951, 269427092488254686881046533485512097791

Offset: 1

Jianing Song, Sep 22 2018

nonn

Primes in A164559.

Companion sequence of A057472. There are 49 terms known in this sequence.

			2*6^1 - 1 = 11, 2*6^2 - 1 = 71, 2*6^3 - 1 = 431, 2*6^4 - 1 = 2591 and 2*6^5 - 1 = 15551 are primes, but 2*6^6 - 1 = 93311 = 23*4057 is not.

K. D. Bajpai, Table of n, a(n) for n = 1..26

Integers k such that 2*b^k - 1 is prime: A090748 (b=2), A003307 (b=3), A120375 (b=5), A057472 (b=6), A002959 (b=7), A002957 (b=10), A120378 (b=11).
Primes of the form 2*b^k - 1: A000668 (b=2), A079363 (b=3), A120376 (b=5), this sequence (b=6), A158795 (b=7), A055558 (b=10), A120377 (b=11).
Cf. also A000043, A002958, A068231, A164559.

[k: n in [1..100] | IsPrime(k) where k is 2*6^n-1];  // K. D. Bajpai, Nov 15 2019

A319535:= n-> (2*6^n-1): select(isprime, [seq((A319535(n), n=1..200))]);  # K. D. Bajpai, Nov 15 2019

Select[Table[2*6^k-1,{k,1600}], PrimeQ[#]&]  (* K. D. Bajpai, Nov 15 2019 *)

for(n=1, 99, my(t); if(ispseudoprime(t=2*6^n-1), print1(t", ")))

a(n) = 2*6^A057472(n) - 1.

A226429 Number of numerical semigroups S of genus 3^n having a minimal generating set of cardinality 2.

Original entry on oeis.org

2, 3, 4, 4, 5, 7, 8, 9, 8, 9, 11, 13, 11, 15, 16, 14, 14, 18, 20, 21

Offset: 1

Arkadiusz Wesolowski, Jun 06 2013

Shalom Eliahou and Jorge Ramírez Alfonsín, Two-generator numerical semigroups and Fermat and Mersenne numbers, SIAM J. Discrete Math., 25(2), 2011, 622-630.

Cf. A003307, A079363.

a(n) = n + 1 if 2*3^n - 1 is prime.

a(n) ~ n + 1.

cp's OEIS Frontend

A319535 Primes of the form 2*6^k - 1.

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