A024639 -id:A024639 - cp's OEIS frontend

A245404 Number of nonnegative integers with property that their base 7/2 expansion (see A024639) has n digits.

7, 21, 70, 245, 861, 3010, 10535, 36876, 129066, 451731, 1581055, 5533696, 19367936, 67787776, 237257216, 830400256, 2906400896, 10172403136, 35603410976, 124611938416, 436141784456, 1526496245596, 5342736859586, 18699579008551, 65448526529925, 229069842854741

Offset: 0

James Van Alstine, Jul 21 2014

			The numbers 7-27 are represented by 20, 21, 22, 23, 24, 25, 26, 40, 41, 42, 43, 44, 45, 46, 60, 61, 62, 63, 64, 65, 66 respectively in base 7/2. These are the only integers with two digits, and so a(2)=21.

Cf. A024639, A081848.

A=[1]
for i in [1..60]:
    A.append(ceil((7-2)/2*sum(A)))
[7*x for x in A]

A245342 Sum of digits of n written in fractional base 7/2.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 2, 3, 4, 5, 6, 7, 8, 4, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 12, 3, 4, 5, 6, 7, 8, 9, 5, 6, 7, 8, 9, 10, 11, 7, 8, 9, 10, 11, 12, 13, 4, 5, 6, 7, 8, 9, 10, 6, 7, 8, 9, 10, 11, 12, 8, 9, 10, 11, 12, 13, 14, 10, 11, 12, 13, 14, 15, 16, 7

Offset: 0

Hailey R. Olafson, Jul 18 2014

The base 7/2 expansion is unique and thus the sum of digits function is well-defined.

			In base 7/2 the number 14 is represented by 40 and so a(14) = 4 + 0 = 4.

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

Cf. A007953, A000120, A024639, A053828, A244040.

a[n_] := a[n] = If[n == 0, 0, a[2 * Floor[n/7]] + Mod[n, 7]]; Array[a, 100, 0] (* Amiram Eldar, Jul 31 2025 *)

a(n) = if(n == 0, 0, a(n\7 * 2) + n % 7); \\ Amiram Eldar, Jul 31 2025

# uses [basepqsum from A245355]
[basepqsum(7,2,w) for w in [0..200]]

a(n) = A007953(A024639(n)).

cp's OEIS Frontend

A245404 Number of nonnegative integers with property that their base 7/2 expansion (see A024639) has n digits.

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A245342 Sum of digits of n written in fractional base 7/2.

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