A344345 - OEIS

%I #7 May 16 2021 02:41:05

%S 3,8,12,14,33,35,39,47,49,51,55,57,59,61,130,132,134,136,140,142,144,

%T 152,156,158,160,176,184,188,190,194,196,198,200,204,206,208,216,220,

%U 222,226,228,230,232,236,238,242,244,246,250,517,521,523,525,529,531,535

%N Digitally balanced numbers in Gray code: numbers whose binary reflected Gray code has the same number of 0's as 1's.

%H Amiram Eldar, <a href="/A344345/b344345.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GrayCode.html">Gray Code</a>.

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Gray_code">Gray code</a>.

%e 8 is a term since its Gray code, 1100, has 2 0's and 2 1's.

%e 33 is a term since its Gray code, 110001, has 3 0's and 3 1's.

%t gc[n_] := gc[n] = If[n <= 1, n, 2^(b = Floor@Log2[n]) + gc[2^(b + 1) - 1 - n]]; gcDigBalQ[n_] := Equal @@ DigitCount[gc[n], 2, {0, 1}]; Select[Range[500], gcDigBalQ]

%Y Cf. A005811, A014550.

%Y Similar sequences: A031443 (binary), A210619 (Zeckendorf), A342727 (base i-1).

%K nonn,base

%O 1,1

%A _Amiram Eldar_, May 15 2021