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A261691 Change of base from fractional base 3/2 to base 3. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

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.

LINKS

Rémy Sigrist, Table of n, a(n) for n = 0..10000

FORMULA

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)

EXAMPLE

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.

PROG

(Sage)

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]]

(PARI) 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

CROSSREFS

Cf. A024629, A007089.

Cf. A005836, A023717, A000695, A037453, A037454, A037455, A037456, A037314.

Cf. A003462, A087088.

Sequence in context: A258826 A157671 A196747 * A351088 A296443 A102046

Adjacent sequences:  A261688 A261689 A261690 * A261692 A261693 A261694

KEYWORD

nonn,base

AUTHOR

Tom Edgar, Aug 28 2015

STATUS

approved

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Last modified September 24 18:53 EDT 2022. Contains 356949 sequences. (Running on oeis4.)