A065362 Rebase n from 4 to 2. Replace 4^k with 2^k in quaternary expansion of n.

1, 2, 3, 2, 3, 4, 5, 4, 5, 6, 7, 6, 7, 8, 9, 4, 5, 6, 7, 6, 7, 8, 9, 8, 9, 10, 11, 10, 11, 12, 13, 8, 9, 10, 11, 10, 11, 12, 13, 12, 13, 14, 15, 14, 15, 16, 17, 12, 13, 14, 15, 14, 15, 16, 17, 16, 17, 18, 19, 18, 19, 20, 21, 8, 9, 10, 11, 10, 11, 12, 13, 12, 13, 14, 15, 14, 15, 16, 17

Offset: 1

Author

Marc LeBrun, Oct 31 2001

Keywords

• base
• easy
• nonn

Comments

Notation: (4)[n](2).

Examples

			24 = 120 -> 1(4) + 2(2) + 0(1) = 8 = a(24).
		

Links

• Harry J. Smith, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A065361.

Programs

Julia

function a(n)
    m, r, b = n, 0, 1
    while m > 0
        m, q = divrem(m, 4)
        r += b * q
        b *= 2
    end
r end; [a(n) for n in 0:79] |> println # Peter Luschny, Jan 03 2021

Mathematica

t = Table[FromDigits[RealDigits[n, 4], 2], {n, 1, 100}] (* Clark Kimberling, Aug 02 2012 *)

PARI

Rebase(x, b, c)= { local(d, e=0, f=1); while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=c); return(e) } { for (n=1, 1000, write("b065362.txt", n, " ", Rebase(n, 4, 2)) ) } \\ Harry J. Smith, Oct 17 2009

Formula

a(n) = 2*a(n/4) if n == 0 (mod 4); otherwise, a(n) = a(n-1) + 1. - Clark Kimberling, Aug 03 2012