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

Author

Rémy Sigrist, Jun 05 2021

Keywords

• nonn
• base

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.

Examples

			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.
		

Links

• 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

Crossrefs

Cf. A342707.

Programs

PARI

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

Formula

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