A344345 Digitally balanced numbers in Gray code: numbers whose binary reflected Gray code has the same number of 0's as 1's.

3, 8, 12, 14, 33, 35, 39, 47, 49, 51, 55, 57, 59, 61, 130, 132, 134, 136, 140, 142, 144, 152, 156, 158, 160, 176, 184, 188, 190, 194, 196, 198, 200, 204, 206, 208, 216, 220, 222, 226, 228, 230, 232, 236, 238, 242, 244, 246, 250, 517, 521, 523, 525, 529, 531, 535

Offset: 1

Author

Amiram Eldar, May 15 2021

Keywords

• nonn
• base

Examples

			8 is a term since its Gray code, 1100, has 2 0's and 2 1's.
33 is a term since its Gray code, 110001, has 3 0's and 3 1's.
		

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Gray Code.
• Wikipedia, Gray code.

Crossrefs

Cf. A005811, A014550.

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

Programs

Mathematica

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]