A324475 k appears t+1 times, where t is the number of trailing zeros in A324474(k).

1, 2, 3, 3, 4, 4, 5, 5, 5, 6, 7, 7, 7, 8, 9, 9, 9, 9, 10, 11, 12, 12, 13, 13, 13, 13, 14, 15, 16, 16, 17, 17, 17, 17, 17, 18, 19, 20, 20, 21, 21, 22, 22, 22, 23, 24, 24, 24, 24, 24, 25, 26, 27, 27, 28, 28, 29, 29, 29, 30, 31, 31, 31, 31, 31, 31, 32, 33, 34, 34

Offset: 1

Author

Nathan Fox and N. J. A. Sloane, Mar 09 2019

Keywords

• nonn
• base

Comments

Interesting because the recurrence is nested one layer deeper than the recurrences for A046699 and A316628.

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Nathan Fox, Trees, Fibonacci Numbers, and Nested Recurrences, Rutgers University Experimental Math Seminar, Mar 07, 2019
• Rémy Sigrist, PARI program for A324475

Crossrefs

Cf. A324474.

A046699, A316628, A324473, A324477 have similar definitions.

Programs

PARI

See Links section.

Formula

For n>3, a(n) = a(n-a(n-1)) + a(n-1-a(n-2)-a(n-2-a(n-2))) + a(n-2-a(n-3)-a(n-3-a(n-3)) - a(n-3-a(n-3)-a(n-3-a(n-3)))). - Nathan Fox, Mar 09 2019 (This formula assumes that a(0) = 0. - Rémy Sigrist, Mar 14 2021)

Extensions

Data corrected and more terms from Rémy Sigrist, Mar 14 2021