A024638 -id:A024638 - cp's OEIS frontend

A245399 Number of nonnegative integers with property that their base 6/5 expansion (see A024638) has n digits.

6, 6, 6, 6, 6, 6, 12, 12, 12, 18, 18, 24, 30, 36, 42, 48, 60, 72, 84, 102, 126, 150, 180, 216, 258, 312, 372, 444, 534, 642, 768, 924, 1110, 1332, 1596, 1914, 2298, 2760, 3312, 3972, 4770, 5724, 6864, 8238, 9888, 11862, 14238, 17082, 20502, 24600, 29520, 35424

Offset: 1

Hailey R. Olafson, Jul 21 2014

			a(3) = 6 because 540, 541, 542, 543, 544 and 545 are the base 6/5 expansions for the integers 12, 13, 14, 15, 16 and 17 respectively and these are the only integers with 3 digits.

G. C. Greubel, Table of n, a(n) for n = 1..1000
Index entries for sequences related to fractional bases

Cf. A024638, A081848, A120170, A245356.

A120170[n_]:= A120170[n] = If[n==1, 1, Ceiling[Sum[A120170[j], {j, n-1}]/5]]; Table[6*A120170[n], {n, 60}] (* G. C. Greubel, Aug 19 2019 *)

A=[1]
for i in [1..60]:
    A.append(ceil(((6-5)/5)*sum(A)))
[6*x for x in A]

a(n) = 6*A120170(n).

A245321 Sum of digits of n written in fractional base 6/5.

Original entry on oeis.org

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

Offset: 0

Tom Edgar, Jul 18 2014

The base 6/5 expansion is unique and thus the sum of digits function is well-defined.

			In base 6/5 the number 15 is represented by 543 and so a(15) = 5 + 4 + 3 = 12.

Amiram Eldar, Table of n, a(n) for n = 0..10000 (terms 0..1000 from G. C. Greubel)
Index entries for sequences related to fractional bases.

Cf. A000120, A007953, A024638, A053827, A244040.

a:= proc(n) `if`(n<1, 0, irem(n, 6, 'q')+a(5*q)) end:
seq(a(n), n=0..100);  # Alois P. Heinz, Aug 19 2019

a[n_]:= a[n] = If[n==0, 0, a[5*Floor[n/6]] + Mod[n,6]]; Table[a[n], {n, 0, 70}] (* G. C. Greubel, Aug 19 2019 *)

a(n) = if(n == 0, 0, a(n\6 * 5) + n % 6); \\ Amiram Eldar, Jul 31 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(6,5,i) for i in [0..70]]

a(n) = A007953(A024638(n)).

cp's OEIS Frontend

A245399 Number of nonnegative integers with property that their base 6/5 expansion (see A024638) has n digits.

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