A037454 a(n) = Sum_{i=0..m} d(i)*6^i, where Sum_{i=0..m} d(i)*3^i is the base 3 representation of n.

0, 1, 2, 6, 7, 8, 12, 13, 14, 36, 37, 38, 42, 43, 44, 48, 49, 50, 72, 73, 74, 78, 79, 80, 84, 85, 86, 216, 217, 218, 222, 223, 224, 228, 229, 230, 252, 253, 254, 258, 259, 260, 264, 265, 266, 288, 289, 290, 294, 295, 296, 300, 301, 302, 432, 433, 434, 438

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Links

• Clark Kimberling, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A037462, A007091, A102491.

Programs

Julia

function a(n)
    m, r, b = n, 0, 1
    while m > 0
        m, q = divrem(m, 3)
        r += b * q
        b *= 6
    end
r end; [a(n) for n in 0:57] |> println # Peter Luschny, Jan 03 2021

Maple

seq(n + (1/2)*add(6^k*floor(n/3^k), k = 1..floor(ln(n)/ln(3))), n = 1..100); # Peter Bala, Dec 01 2016

Mathematica

t = Table[FromDigits[RealDigits[n, 3], 6], {n, 0, 100}]
(* Clark Kimberling, Aug 03 2012 *)

Formula

From Peter Bala, Dec 01 2016: (Start)

a(n) = n + 1/2*Sum_{k >= 1} 6^k*floor(n/3^k). Cf. A037462, A007091 and A102491.

a(0) = 0; a(n) = 6*a(n/3) if n == 0 (mod 3) else a(n) = a(n-1) + 1. (End)

Extensions

Offset changed to 0 by Clark Kimberling, Aug 03 2012