A024643 -id:A024643 - cp's OEIS frontend

A245402 Number of nonnegative integers with property that their base 7/6 expansion (see A024643) has n digits.

7, 7, 7, 7, 7, 7, 7, 14, 14, 14, 21, 21, 28, 28, 35, 42, 49, 56, 63, 77, 91, 105, 119, 140, 161, 189, 224, 259, 301, 350, 413, 483, 560, 651, 763, 889, 1036, 1211, 1414, 1645, 1925, 2240, 2618, 3052, 3563, 4158, 4851, 5656, 6601, 7700, 8981, 10479, 12229, 14266

Offset: 1

Hailey R. Olafson, Jul 21 2014

			a(3) = 7 because 650, 651, 652, 653, 654, 655 and 656 are the base 7/6 expansions for the integers 14, 15, 16, 17, 18, 19 and 20 respectively and these are the only integers with 3 digits.

Cf. A024643, A120178, A072493, A245356.

A=[1]
for i in [1..60]:
    A.append(ceil(((7-6)/6)*sum(A)))
[7*x for x in A]

a(n) = 7*A120178(n).

A245337 Sum of digits of n in fractional base 7/6.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 6, 7, 8, 9, 10, 11, 12, 11, 12, 13, 14, 15, 16, 17, 15, 16, 17, 18, 19, 20, 21, 18, 19, 20, 21, 22, 23, 24, 20, 21, 22, 23, 24, 25, 26, 21, 22, 23, 24, 25, 26, 27, 21, 22, 23, 24, 25, 26, 27, 27, 28, 29, 30, 31, 32, 33, 26, 27, 28, 29, 30

Offset: 0

James Van Alstine, Jul 18 2014

The base 7/6 expansion is unique and thus the sum of digits function is well-defined.

			In base 7/6 the number 7 is represented by 60 and so a(7) = 6+0 = 6.

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

Cf. A024643, A007953, A053828.

a[n_] := a[n] = If[n == 0, 0, a[6 * Floor[n/7]] + Mod[n, 7]]; Array[a, 100, 0] (* Amiram Eldar, Jul 31 2025 *)

a(n) = if(n == 0, 0, a(n\7 * 6) + n % 7); \\ Amiram Eldar, Jul 31 2025

# uses [basepqsum from A245355]
[basepqsum(7,6,y) for y in [0..200]]

a(n) = A007953(A024643(n)). - Amiram Eldar, Jul 31 2025

A245477 Period 6: repeat [1, 1, 1, 1, 1, 2].

Original entry on oeis.org

1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1

Offset: 0

Hailey R. Olafson, Jul 23 2014

First differences of A047368. The first differences of this sequence are in A131533. - Wesley Ivan Hurt, Jul 24 2014

Binomial Transform of a(n) gives: 1, 2, 4, 8, 16, 33, 70, 149, 312, 638, 1276, 2511, ... - Wesley Ivan Hurt, Aug 13 2014

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Cf. A024643, A047368, A097325, A130782, A131534, A172051, A177702, A177704, A177706.

[Floor((n+1)*7/6) - Floor((n)*7/6) : n in [0..100]]; // Wesley Ivan Hurt, Aug 06 2014

A:= n -> piecewise(n mod 6 = 5, 2, 1);
seq(A(n), n=0..100); # Robert Israel, Jul 23 2014

Table[2 - Sign[Mod[n + 1, 6]], {n, 0, 100}] (* Wesley Ivan Hurt, Jul 24 2014 *)
PadRight[{},120,{1,1,1,1,1,2}] (* Harvey P. Dale, Jun 02 2016 *)

a(n) = 7*(n+1)\6 - 7*n\6; \\ Michel Marcus, Jul 23 2014

[floor((n+1)*7/6) - floor((n)*7/6) for n in [0..200]]

a(n) = floor((n+1)*7/6) - floor((n)*7/6).
G.f.: 1/(1-x) + x^5/(1-x^6). - Robert Israel, Jul 23 2014
From Wesley Ivan Hurt, Jul 24 2014, Aug 06-29 2014: (Start)
  a(n) = 2 - sign((n+1) mod 6).
  a(n) = 3 - 2^sign((n+1) mod 6).
  a(n) = A172051(n) + 1.
  a(2n) = 1, a(2n+1) = A177702(n).
  Sum_{i=0..n-2} a(i) = A047368(n), n>0.
  a(n) = 1 + mod(n, 1 + mod(n-1, 3)).
  a(n) = 1 + binomial(mod(5n + 10, 6), 5). (End)
From Wesley Ivan Hurt, Jun 23 2016: (Start)
a(n) = a(n-6) for n>5.
a(n) = (7 - cos(n*Pi) + cos(n*Pi/3) - cos(2*n*Pi/3) - sqrt(3)*sin(n*Pi/3) - sqrt(3)*sin(2*n*Pi/3))/6. (End)

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A245402 Number of nonnegative integers with property that their base 7/6 expansion (see A024643) has n digits.

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A245337 Sum of digits of n in fractional base 7/6.

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A245477 Period 6: repeat [1, 1, 1, 1, 1, 2].

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