A024632 -id:A024632 - cp's OEIS frontend

A245415 Number of nonnegative integers with property that their base 5/2 expansion (see A024632) has n digits.

5, 10, 25, 60, 150, 375, 940, 2350, 5875, 14685, 36715, 91785, 229465, 573660, 1434150, 3585375, 8963440, 22408600, 56021500, 140053750, 350134375, 875335935, 2188339840, 5470849600, 13677124000, 34192810000, 85482025000, 213705062500, 534262656250

Offset: 1

Hailey R. Olafson, Jul 21 2014

			a(2) = 10 because  20, 21, 22, 23, 24, 40, 41, 42, 43 and 44 are the base 5/2 expansions for the integers 5, 6, 7, 8, 9, 10, 11, 12, 13 and 14 respectively and these are the only integers with 2 digits.

Cf. A081848, A245356, A024632.

A=[1]
for i in [1..60]:
    A.append(ceil(((5-2)/2)*sum(A)))
[5*x for x in A]

A245341 Sum of digits of n written in fractional base 5/2.

Original entry on oeis.org

0, 1, 2, 3, 4, 2, 3, 4, 5, 6, 4, 5, 6, 7, 8, 3, 4, 5, 6, 7, 5, 6, 7, 8, 9, 4, 5, 6, 7, 8, 6, 7, 8, 9, 10, 8, 9, 10, 11, 12, 4, 5, 6, 7, 8, 6, 7, 8, 9, 10, 5, 6, 7, 8, 9, 7, 8, 9, 10, 11, 9, 10, 11, 12, 13, 5, 6, 7, 8, 9, 7, 8, 9, 10, 11, 6, 7, 8, 9, 10, 8, 9

Offset: 0

James Van Alstine, Jul 18 2014

The base 5/2 expansion is unique and thus the sum of digits function is well-defined.

			In base 5/2 the number 7 is represented by 22 and so a(7) = 2+2 = 4.

Alois P. Heinz, Table of n, a(n) for n = 0..10000
Index entries for sequences related to fractional bases.

Cf. A024632, A007953, A053824, A215088.

a:= proc(n) `if`(n<1, 0, irem(n, 5, 'q')+a(2*q)) end:
seq(a(n), n=0..81);  # Alois P. Heinz, May 14 2021

a[n_] := a[n] = If[n == 0, 0, a[2 * Floor[n/5]] + Mod[n, 5]]; Array[a, 100, 0] (* Amiram Eldar, Jul 30 2025 *)

a(n) = if(n == 0, 0, a(n\5 * 2) + n % 5); \\ Amiram Eldar, Jul 30 2025

# uses [basepqsum from A245355]
[basepqsum(5,2,y) for y in [0..200]]

a(n) = A007953(A024632(n)). - Amiram Eldar, Jul 30 2025

Definition corrected by Georg Fischer, May 14 2021

cp's OEIS Frontend

A245415 Number of nonnegative integers with property that their base 5/2 expansion (see A024632) has n digits.

Views

Author

Keywords

Examples

Crossrefs

Programs

Sage

A245341 Sum of digits of n written in fractional base 5/2.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Sage

Formula

Extensions