A024647 -id:A024647 - cp's OEIS frontend

A245420 Number of nonnegative integers with property that their base 8/5 expansion (see A024647) has n digits.

8, 8, 16, 24, 40, 64, 96, 160, 256, 408, 648, 1040, 1664, 2664, 4264, 6816, 10912, 17456, 27928, 44688, 71496, 114400, 183040, 292864, 468576, 749728, 1199560, 1919296, 3070872, 4913400, 7861440, 12578304, 20125288, 32200456, 51520728, 82433168, 131893072

Offset: 1

Tom Edgar, Jul 21 2014

			a(2) = 8 because 50, 51, 52, 53, 54, 55, 56, and 57 are the base 8/5 expansions for the numbers 8-15 respectively and these are the only integers with 2 digits.

Cf. A024647, A245356, A081848.

A=[1]
for i in [1..100]:
    A.append(ceil(((8-5)/5)*sum(A)))
[8*x for x in A]

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

Original entry on oeis.org

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

Tom Edgar, Jul 18 2014

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

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

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

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

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 *)

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

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]]

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

cp's OEIS Frontend

A245420 Number of nonnegative integers with property that their base 8/5 expansion (see A024647) has n digits.

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

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