A244040 Sum of digits of n in fractional base 3/2.

0, 1, 2, 2, 3, 4, 3, 4, 5, 3, 4, 5, 5, 6, 7, 4, 5, 6, 5, 6, 7, 7, 8, 9, 5, 6, 7, 5, 6, 7, 7, 8, 9, 8, 9, 10, 5, 6, 7, 7, 8, 9, 6, 7, 8, 7, 8, 9, 9, 10, 11, 9, 10, 11, 5, 6, 7, 7, 8, 9, 8, 9, 10, 6, 7, 8, 8, 9, 10, 8, 9, 10, 9, 10, 11, 11, 12, 13, 10, 11, 12, 5

Offset: 0

Author

James Van Alstine, Jun 17 2014

Keywords

• nonn
• base
• easy

Comments

The base 3/2 expansion is unique, and thus the sum of digits function is well-defined.

Fixed point starting with 0 of the two-block substitution a,b -> a,a+1,a+2 for a = 0,1,2,... and b = 0,1,2,.... - Michel Dekking, Sep 29 2022

Examples

			In base 3/2 the number 7 is represented by 211 and so a(7) = 2 + 1 + 1 = 4.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Michel Dekking, The Thue-Morse sequence in base 3/2, J. Int. Seq., Vol. 26 (2023), Article 23.2.3; arXiv preprint, arXiv:2301.13563 [math.CO], 2023.
• Index entries for sequences related to fractional bases.

Crossrefs

Cf. A024629, A007953, A000120, A053735, A244041, A246435.

Programs

Haskell

a244040 0 = 0
a244040 n = a244040 (2 * n') + t where (n', t) = divMod n 3
-- Reinhard Zumkeller, Sep 05 2014

Mathematica

a[n_]:= a[n]= If[n==0, 0, a[2*Floor[n/3]] + Mod[n,3]]; Table[a[n], {n, 0, 85}] (* G. C. Greubel, Aug 20 2019 *)

PARI

a(n) = if(n == 0, 0, a(n\3 * 2) + n % 3); \\ Amiram Eldar, Jul 30 2025

Python

a244040 = lambda n: a244040((n // 3) * 2) + (n % 3) if n else 0 # David Radcliffe, Aug 21 2021

Sage

def base32sum(n):
    L, i = [n], 1
    while L[i-1]>2:
        x=L[i-1]
        L[i-1]=x.mod(3)
        L.append(2*floor(x/3))
        i+=1
    return sum(L)
[base32sum(n) for n in [0..85]]

Formula

a(0) = 0, a(3n+r) = a(2n)+r for n >= 0 and r = 0, 1, 2. - David Radcliffe, Aug 21 2021

a(n) = A007953(A024629(n)). - Amiram Eldar, Jul 30 2025