A345021 a(n) is the result of replacing 2's by 0's in the hereditary base-2 expansion of n.

0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1, 2, 0, 1, 0, 1, 1, 2, 1

Offset

0,6

Comments

The 0's in hereditary base-2 expansions appear at leaf positions.

This sequence is unbounded:

- let b(1) = 2^0, and for any n > 1, b(n+1) = 2^2^b(n),

- a(b(n)) = 1 for any n > 0,

- a(Sum_{k = 1..n} b(k)) = n.

Links

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

Rémy Sigrist, Colored scatterplot of the ordinal transform of the first 2^14 terms

Rémy Sigrist, Colored scatterplot of the ordinal transform of the first 2^17 terms

Wikipedia, Hereditary base-n notation

Formula

a(n) = A342707(n, 0).

Example

For n = 13:
- 13 = 2^(2^2^0 + 2^0) + 2^2^2^0 + 2^0,
- so a(13) = 0^(0^0^0 + 0^0) + 0^0^0^0 + 0^0 = 2.

Prog

(PARI) a(n) = { my (v=0, e); while (n, n-=2^e=valuation(n, 2); v+=0^a(e)); v }

Crossrefs

Cf. A342707.

Sequence in context: A283760 A070088 A131851 * A104886 A215604 A139351

Adjacent sequences: A345018 A345019 A345020 * A345022 A345023 A345024

Keyword

nonn,base

Author

Rémy Sigrist, Jun 05 2021

Status

approved