A037456 -id:A037456 - cp's OEIS frontend

0, 1, 2, 6, 7, 8, 21, 22, 23, 63, 64, 65, 69, 70, 71, 192, 193, 194, 207, 208, 209, 213, 214, 215, 579, 580, 581, 621, 622, 623, 627, 628, 629, 642, 643, 644, 1737, 1738, 1739, 1743, 1744, 1745, 1866, 1867, 1868, 1881, 1882, 1883, 1887, 1888, 1889, 1929, 1930

Offset: 0

Tom Edgar, Aug 28 2015

To obtain a(n), we interpret A024629(n) as a base 3 representation (instead of base 3/2). More precisely, if A024629(n) = A007089(m), then a(n) = m.

The digits used in fractional base 3/2 are 0, 1, and 2, which are the same as the digits used in base 3.

			The base 3/2 representation of 7 is (2,1,1); i.e., 7 = 2*(3/2)^2 + 1*(3/2) + 1. Since 2*(3^2) + 1*3 + 1*1 = 22, we have a(7) = 22.

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

Cf. A024629, A007089.
Cf. A005836, A023717, A000695, A037453, A037454, A037455, A037456, A037314.
Cf. A003462, A087088.

a[n_] := a[n] = If[n == 0, 0, 3 * a[2 * Floor[n/3]] + Mod[n, 3]]; Array[a, 100, 0] (* Amiram Eldar, Aug 04 2025 *)

a(n) = { my (v=0, t=1); while (n, v+=t*(n%3); n=(n\3)*2; t*=3); v } \\ Rémy Sigrist, Apr 06 2021

def changebase(n):
    L=[n]
    i=1
    while L[i-1]>2:
        x=L[i-1]
        L[i-1]=x.mod(3)
        L.append(2*floor(x/3))
        i+=1
    return sum([L[i]*3^i for i in [0..len(L)-1]])
[changebase(n) for n in [0..100]]

For n = Sum_{i=0..m} c_i*(3/2)^i with each c_i in {0,1,2}, a(n) = Sum_{i=0..m} c_i*3^i.
From Rémy Sigrist, Apr 06 2021: (Start)
Apparently:
- a(3*n) = a(3*n-1) + A003462(1+A087088(n)) for any n > 0,
- a(3*n+1) = a(3*n) + 1 for any n >= 0,
- a(3*n+2) = a(3*n+1) + 1 for any n >= 0,
(End)

cp's OEIS Frontend

A261691 Change of base from fractional base 3/2 to base 3.

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