A336720 -id:A336720 - cp's OEIS frontend

A336719 Largest odd prime p for which the order of 2 mod p is at most n.

3, 7, 7, 31, 31, 127, 127, 127, 127, 127, 127, 8191, 8191, 8191, 8191, 131071, 131071, 524287, 524287, 524287, 524287, 524287, 524287, 524287, 524287, 524287, 524287, 524287, 524287, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647, 2147483647

Offset: 2

Jeppe Stig Nielsen, Aug 01 2020

nonn

a(1) is undefined.
Changing "at most n" to "equal to n" in the definition gives A097406.
The first term that is not a Mersenne prime (A000668) is 4432676798593.
For a version without duplicates, see A336720. For a list of all n where a(n) increases, see A336721.

Jeppe Stig Nielsen, Table of n, a(n) for n = 2..251

Cf. A000668, A005420, A014664, A097406, A336720, A336721.

re=0;for(n=2,+oo,p=vecmax(factor(2^n-1)[,1]);p>re&&re=p;print1(re,", "))

A336721 Values k where A336719(k) increases.

Original entry on oeis.org

2, 3, 5, 7, 13, 17, 19, 31, 49, 61, 83, 89, 107, 127, 167, 179, 197, 233, 241, 269, 281, 347, 373, 421, 443, 457, 487, 521, 607, 697, 769, 829, 881, 1049, 1063

Offset: 1

Jeppe Stig Nielsen, Aug 01 2020

Also, values k (record positions) where A005420(k) reaches a new maximum. For the maximum itself, see A336720.

A000043 is a subsequence.

Cf. A000043, A005420, A336719, A336720.

re=0;for(k=2,+oo,p=vecmax(factor(2^k-1)[,1]);if(p>re,re=p;print1(k,", ")))

cp's OEIS Frontend

A336719 Largest odd prime p for which the order of 2 mod p is at most n.

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