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

%I A245355 #14 Aug 02 2025 06:25:23
%S A245355 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,
%T A245355 16,17,18,19,11,12,13,14,15,16,17,18,13,14,15,16,17,18,19,20,18,19,20,
%U A245355 21,22,23,24,25,14,15,16,17,18,19,20,21,13,14,15,16,17
%N A245355 Sum of digits of n written in fractional base 8/5.
%C A245355 The base 8/5 expansion is unique and thus the sum of digits function is well-defined.
%H A245355 Amiram Eldar, <a href="/A245355/b245355.txt">Table of n, a(n) for n = 0..10000</a>
%H A245355 <a href="/index/Ba#base_fractional">Index entries for sequences related to fractional bases</a>.
%F A245355 a(n) = A007953(A024647(n)).
%e A245355 In base 8/5 the number 20 is represented by 524 and so a(20) = 5 + 2 + 4 = 11.
%t A245355 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 *)
%o A245355 (Sage)
%o A245355 def basepqsum(p, q, n):
%o A245355     L = [n]
%o A245355     i = 1
%o A245355     while L[i-1]>=p:
%o A245355         x=L[i-1]
%o A245355         L[i-1]=x.mod(p)
%o A245355         L.append(q*(x//p))
%o A245355         i+=1
%o A245355     return sum(L)
%o A245355 [basepqsum(8,5,i) for i in [0..100]]
%o A245355 (PARI) a(n) = if(n == 0, 0, a(n\8 * 5) + n % 8); \\ _Amiram Eldar_, Aug 02 2025
%Y A245355 Cf. A000120, A007953, A024647, A053829, A244040.
%K A245355 nonn,base,easy
%O A245355 0,3
%A A245355 _Tom Edgar_, Jul 18 2014