A037462 - OEIS

%I #16 Dec 01 2016 11:25:30

%S 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,

%T 81,82,83,88,89,90,91,128,129,130,131,136,137,138,139,144,145,146,147,

%U 152,153,154,155,192,193,194,195,200,201,202,203,208,209,210

%N 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.

%H Clark Kimberling, <a href="/A037462/b037462.txt">Table of n, a(n) for n = 0..1000</a>

%F From _Peter Bala_, Dec 01 2016: (Start):

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

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

%p 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

%t Table[FromDigits[RealDigits[n, 4], 8], {n, 0, 100}]

%t (* _Clark Kimberling_, Aug 14 2012 *)

%Y Cf. A037454, A007091, A102491.

%K nonn,base,easy

%O 0,3

%A _Clark Kimberling_

%E Offset changed to 0 by _Clark Kimberling_, Aug 14 2012