A245355 Sum of digits of n written in fractional base 8/5.

0, 1, 2, 3, 4, 5, 6, 7, 5, 6, 7, 8, 9, 10, 11, 12, 7, 8, 9, 10, 11, 12, 13, 14, 12, 13, 14, 15, 16, 17, 18, 19, 11, 12, 13, 14, 15, 16, 17, 18, 13, 14, 15, 16, 17, 18, 19, 20, 18, 19, 20, 21, 22, 23, 24, 25, 14, 15, 16, 17, 18, 19, 20, 21, 13, 14, 15, 16, 17

Offset: 0

Author

Tom Edgar, Jul 18 2014

Keywords

• nonn
• base
• easy

Comments

The base 8/5 expansion is unique and thus the sum of digits function is well-defined.

Examples

			In base 8/5 the number 20 is represented by 524 and so a(20) = 5 + 2 + 4 = 11.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to fractional bases.

Crossrefs

Cf. A000120, A007953, A024647, A053829, A244040.

Programs

Mathematica

a[n_] := a[n] = If[n == 0, 0, a[5 * Floor[n/8]] + Mod[n, 8]]; Array[a, 100, 0] (* Amiram Eldar, Aug 02 2025 *)

PARI

a(n) = if(n == 0, 0, a(n\8 * 5) + n % 8); \\ Amiram Eldar, Aug 02 2025

Sage

def basepqsum(p, q, n):
    L = [n]
    i = 1
    while L[i-1]>=p:
        x=L[i-1]
        L[i-1]=x.mod(p)
        L.append(q*(x//p))
        i+=1
    return sum(L)
[basepqsum(8,5,i) for i in [0..100]]

Formula

a(n) = A007953(A024647(n)).