A246435 Length of representation of n in fractional base 3/2.

1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9

Offset: 0

Author

Reinhard Zumkeller, Sep 05 2014

Keywords

• nonn
• base
• easy

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• B. Chen, R. Chen, J. Guo, S. Lee et al., On Base 3/2 and its sequences, arXiv:1808.04304 [math.NT], 2018.
• Index entries for sequences related to fractional bases.

Crossrefs

Cf. A024629, A055642, A070989, A081604, A081848 (run lengths), A244040.

Programs

Haskell

a246435 n = if n < 3 then 1 else a246435 (2 * div n 3) + 1
-- Reinhard Zumkeller, Sep 05 2014

Mathematica

a[n_] := If[n < 3, 1, a[2 Quotient[n, 3]] + 1]; Array[a, 100, 0] (* Jean-François Alcover, Feb 05 2019 *)

PARI

a(n) = if(n < 3, 1, a(n\3 * 2) + 1); \\ Amiram Eldar, Jul 30 2025

Formula

a(n) = if n < 3 then 1, otherwise a(2*floor(n/3)) + 1.

a(n) = A055642(A024629(n)).