A024662 -id:A024662 - cp's OEIS frontend

A245351 Sum of digits of n written in fractional base 10/7.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 21, 22, 23, 24, 25, 26, 27, 28

Offset: 0

Hailey R. Olafson, Jul 18 2014

The base 10/7 expansion is unique and thus the sum of digits function is well-defined.

			In base 10/7 the number 14 is represented by 74 and so a(14) = 7 + 4 = 11.

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

Cf. A000120, A007953, A024662, A244040.

a[n_] := a[n] = If[n == 0, 0, a[7 * Floor[n/10]] + Mod[n, 10]]; Array[a, 100, 0] (* Amiram Eldar, Aug 04 2025 *)

a(n) = if(n == 0, 0, a(n\10 * 7) + n % 10); \\ Amiram Eldar, Aug 04 2025

# uses [basepqsum from A245355]
[basepqsum(10,7,w) for w in [0..200]]

a(n) = A007953(A024662(n)).

A245431 Number of nonnegative integers with property that their base 10/7 expansion has n digits.

Original entry on oeis.org

10, 10, 10, 20, 30, 40, 60, 80, 120, 170, 240, 340, 490, 700, 1000, 1430, 2040, 2910, 4160, 5940, 8490, 12130, 17330, 24750, 35360, 50520, 72170, 103100, 147280, 210400, 300570, 429390, 613410, 876300, 1251860, 1788370, 2554820, 3649740, 5213910, 7448450

Offset: 1

Hailey R. Olafson, Jul 21 2014

See A024662 for an explanation of base 10/7.

			a(2) = 10 because 70, 71, 72, 73, 74, 75, 76, 77, 78 and 79 are the base 10/7 expansions for the integers 10, 11, 12, 13, 14, 15, 16, 17, 18 and 19 respectively and these are the only integers with 2 digits.

Cf. A024662, A081848, A245356.

A=[1]
for i in [1..60]:
    A.append(ceil(((10-7)/7)*sum(A)))
[10*x for x in A]

cp's OEIS Frontend

A245351 Sum of digits of n written in fractional base 10/7.

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