A037462 a(n) = Sum_{i = 0..m} d(i)*8^i, where Sum_{i = 0..m} d(i)*4^i is the base 4 representation of n.

0, 1, 2, 3, 8, 9, 10, 11, 16, 17, 18, 19, 24, 25, 26, 27, 64, 65, 66, 67, 72, 73, 74, 75, 80, 81, 82, 83, 88, 89, 90, 91, 128, 129, 130, 131, 136, 137, 138, 139, 144, 145, 146, 147, 152, 153, 154, 155, 192, 193, 194, 195, 200, 201, 202, 203, 208, 209, 210

Offset: 0

Author

Clark Kimberling

Keywords

• nonn
• base
• easy

Links

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

Crossrefs

Cf. A037454, A007091, A102491.

Programs

Maple

seq(n + (1/2)*add(8^k*floor(n/4^k), k = 1..floor(ln(n)/ln(4))), n = 1..100); # Peter Bala, Dec 01 2016

Mathematica

Table[FromDigits[RealDigits[n, 4], 8], {n, 0, 100}]
(* Clark Kimberling, Aug 14 2012 *)

Formula

From Peter Bala, Dec 01 2016: (Start):

a(n) = n + 1/2*Sum_{k >= 1} 8^k*floor(n/4^k). Cf. A037454, A007091 and A102491.

a(0) = 0; a(n) = 8*a(n/4) if n == 0 (mod 4) else a(n) = a(n-1) + 1. (End)

Extensions

Offset changed to 0 by Clark Kimberling, Aug 14 2012