

A329221


a(0)=0. If a(n)=k is the first occurrence of k then a(n+1)=a(k), otherwise a(n+1)=nm where m is the index of the greatest prior term.


0



0, 0, 1, 0, 1, 2, 1, 1, 2, 3, 0, 1, 2, 3, 4, 1, 1, 2, 3, 4, 5, 2, 1, 2, 3, 4, 5, 6, 1, 1, 2, 3, 4, 5, 6, 7, 1, 1, 2, 3, 4, 5, 6, 7, 8, 2, 1, 2, 3, 4, 5, 6, 7, 8, 9, 3, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 1, 1, 2, 3, 4, 5, 6, 7, 8
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OFFSET

0,6


COMMENTS

Subsequence a(A000217(k+1)), k>=0 is an identical copy of the original. Erasure of the first occurrence of every k does not reproduce the original so this is not a fractal sequence. However, if a(0) and the copy subsequence are both erased, what remains is A002260. Hence this sequence contains both a copy identical to the original, and a fractal subsequence different from the original.


LINKS

Table of n, a(n) for n=0..86.
Wikipedia, Fractal sequence


FORMULA

a(k) = a(A000217(k+1)), k >= 0.
The nth occurrence of k is a((k^2 + (2*n+1)*k + n*(n1))/2), k >= 1.
The nth occurrence of 0 is a(A072638(n)), n >= 0.


EXAMPLE

a(0)=0 is the first occurrence of the term 0, therefore a(1)=a(0+1)=a(0)=0. a(1)=0 has been seen before, and 0 is the index of the greatest prior term (0), so a(2)=a(1+1)=10=1.


CROSSREFS

Cf. A000217, A002260, A181391, A072638.
Sequence in context: A306512 A239397 A307884 * A177858 A166967 A136256
Adjacent sequences: A329218 A329219 A329220 * A329222 A329223 A329224


KEYWORD

nonn


AUTHOR

David James Sycamore, Nov 22 2019


STATUS

approved



