cp's OEIS Frontend

For n <= 255, computed using R. J. Mathar's Maple programs from A051775. a(256) = 21845 from J. H. Conway and Alex Ryba, May 04 2012

Apparently, all terms belong to A001317, and A001317(k) appears 2^k times. - Rémy Sigrist, Jun 14 2020

From Jianing Song, Aug 10 2022: (Start)

The observation above is incorrect. Note that {0,1,...,2^2^k-1} together with the nim operations makes a field isomorphic to GF(2^2^k). This means that:

- Every number is a divisor of a number of the form 2^2^k-1, and every divisor of 2^2^k-1 for some k appears;

- If d is a divisor of 2^2^k-1 for some k, then d appears phi(d) times among {a(1),a(2),...,a(2^2^m-1)} for all m >= k, phi = A000010. This means that if d > 1, and k is the smallest number such that d | 2^2^k-1, then d can only appear among {a(2^2^(k-1)),...a(2^2^k-1)}.

So the correct result should be: all terms are divisors of numbers of the form 2^2^k-1, and each divisor d appears phi(d) times.

For example, 641 would appear 640 times in this sequence, among {a(2^32),...,a(2^64-1)}, although to determine their positions is hard. (End)

This is a permutation of A094358.