A245321 - OEIS

%I #27 Aug 08 2023 09:13:04

%S 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,

%T 17,18,19,15,16,17,18,19,20,15,16,17,18,19,20,20,21,22,23,24,25,19,20,

%U 21,22,23,24,23,24,25,26,27,28,21,22,23,24,25,26,24,25

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

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

%H G. C. Greubel, <a href="/A245321/b245321.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Ba#base_fractional">Index entries for sequences related to fractional bases</a>

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

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

%p a:= proc(n) `if`(n<1, 0, irem(n, 6, 'q')+a(5*q)) end:

%p seq(a(n), n=0..100);  # _Alois P. Heinz_, Aug 19 2019

%t 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 *)

%o (Sage)

%o def basepqsum(p,q,n):

%o     L=[n]

%o     i=1

%o     while L[i-1]>=p:

%o         x=L[i-1]

%o         L[i-1]=x.mod(p)

%o         L.append(q*(x//p))

%o         i+=1

%o     return sum(L)

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

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

%K nonn,base

%O 0,3

%A _Tom Edgar_, Jul 18 2014