A245321 Sum of digits of n written in fractional base 6/5.

0, 1, 2, 3, 4, 5, 5, 6, 7, 8, 9, 10, 9, 10, 11, 12, 13, 14, 12, 13, 14, 15, 16, 17, 14, 15, 16, 17, 18, 19, 15, 16, 17, 18, 19, 20, 15, 16, 17, 18, 19, 20, 20, 21, 22, 23, 24, 25, 19, 20, 21, 22, 23, 24, 23, 24, 25, 26, 27, 28, 21, 22, 23, 24, 25, 26, 24, 25

Offset

0,3

Comments

The base 6/5 expansion is unique and thus the sum of digits function is well-defined.

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for sequences related to fractional bases

Formula

a(n) = A007953(A024638(n)).

Example

In base 6/5 the number 15 is represented by 543 and so a(15) = 5 + 4 + 3 = 12.

Maple

a:= proc(n) `if`(n<1, 0, irem(n, 6, 'q')+a(5*q)) end:
seq(a(n), n=0..100);  # Alois P. Heinz, Aug 19 2019

Mathematica

a[n_]:= a[n] = If[n==0, 0, a[5*Floor[n/6]] + Mod[n, 6]]; Table[a[n], {n, 0, 70}] (* G. C. Greubel, Aug 19 2019 *)

Prog

(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(6, 5, i) for i in [0..70]]

Crossrefs

Cf. A000120, A007953, A024638, A053827, A244040.

Sequence in context: A195181 A003005 A332204 * A006163 A331268 A053757

Adjacent sequences: A245318 A245319 A245320 * A245322 A245323 A245324

Keyword

nonn,base

Author

Tom Edgar, Jul 18 2014

Status

approved