A292237 -id:A292237 - cp's OEIS frontend

A291691 Primes p such that gpf(lpf(2^p - 1) - 1) = p.

2, 3, 5, 7, 11, 13, 23, 29, 37, 43, 47, 53, 73, 79, 83, 97, 113, 131, 151, 173, 179, 181, 191, 197, 211, 223, 233, 239, 251, 263, 277, 281, 283, 307, 317, 337, 353, 359, 367, 383, 397, 419, 431, 439, 443, 457, 461, 463, 467, 487, 491, 499

Offset: 1

Thomas Ordowski, Aug 30 2017

nonn

This sequence has not been proved to be infinite.
The terms p such that 2^p - 1 is a Mersenne prime are 2, 3, 5, 7, and 13.
If p is prime, then gpf(lpf(2^p - 1) - 1) >= p.
Primes q such that gpf(lpf(2^q - 1) - 1) > q are A292237.

			We have gpf(lpf(2^11 - 1) - 1) = gpf(23 - 1) = 11, so 11 is a term.

Charles R Greathouse IV, Table of n, a(n) for n = 1..119

Cf. A000040, A000043, A006530, A016047, A020639, A236128.

Contains A002515.

lpf[n_] := FactorInteger[n][[1, 1]]; gpf[n_] := FactorInteger[n][[-1, 1]]; Select[ Prime@ Range@ 45, gpf[lpf[2^# - 1] - 1] == # &] (* Giovanni Resta, Aug 30 2017 *)

listp(nn) = forprime(p=2, nn, if (vecmax(factor(vecmin(factor(2^p-1)[,1])-1)[,1]) == p, print1(p, ", "));); \\ Michel Marcus, Aug 30 2017

a(17)-a(26) from Michel Marcus, Aug 30 2017
a(27)-a(34) from Giovanni Resta, Aug 30 2017
a(35)-a(52) from Charles R Greathouse IV, Aug 30 2017

A292238 a(n) = gpf(lpf(2^prime(n) - 1) - 1) where prime(n) is the n-th prime.

Original entry on oeis.org

2, 3, 5, 7, 11, 13, 257, 73, 23, 29, 331, 37, 163, 43, 47, 53, 61, 1321, 2677, 1609, 73, 79, 83, 2931542417, 97, 278557, 599, 28059810762433, 31981, 113, 77158673929, 131, 27977333, 457, 37888318897441, 151, 4523, 461, 541, 173, 179, 181, 191, 587, 197, 3690437

Offset: 1

Michel Marcus, Sep 12 2017

nonn

Cf. A001348, A291691, A292237.

a(n) = vecmax(factor(vecmax(factor(2^prime(n)-1)[, 1])-1)[, 1]);

For p in A291691, let pp be such that p = prime(pp), then a(pp) = p.

cp's OEIS Frontend

A291691 Primes p such that gpf(lpf(2^p - 1) - 1) = p.

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