A359088 Odd integers k such that the multiplicative order of 2 modulo the largest prime factor of 2^k - 1 is different from k.

51, 111, 327, 1281, 1563

Offset: 1

Author

Michel Marcus, Dec 16 2022

Keywords

• nonn
• hard
• more

Comments

In other words, odd integers k that are not equal to A002326((A005420(k)-1)/2).

Inspired by former comment from Thomas Ordowski in A005420.

Crossrefs

Cf. A002326, A005420.

Programs

PARI

zn(n) = znorder(Mod(2, 2*n+1)); \\ A002326
f(n) = vecmax(factor(2^n-1)[,1]); \\ A005420
isok(k) = (k%2) && (zn((f(k)-1)/2) != k);

Extensions

Edited and a(4)-a(5) added by Max Alekseyev, Feb 16 2025