A332498 a(n) = y(w+1) where y(0) = 0 and y(k+1) = 2^(k+1)-1-y(k) (resp. y(k)) when d_k = 2 (resp. d_k <> 2) and Sum_{k=0..w} d_k*3^k is the ternary representation of n. Sequence A332497 gives corresponding x's.

0, 0, 1, 0, 0, 1, 3, 3, 2, 0, 0, 1, 0, 0, 1, 3, 3, 2, 7, 7, 6, 7, 7, 6, 4, 4, 5, 0, 0, 1, 0, 0, 1, 3, 3, 2, 0, 0, 1, 0, 0, 1, 3, 3, 2, 7, 7, 6, 7, 7, 6, 4, 4, 5, 15, 15, 14, 15, 15, 14, 12, 12, 13, 15, 15, 14, 15, 15, 14, 12, 12, 13, 8, 8, 9, 8, 8, 9, 11, 11

Offset: 0

Author

Rémy Sigrist, Feb 14 2020

Keywords

• nonn
• base

Examples

			For n = 42:
- the ternary representation of 42 is "1120",
- x(0) = 0,
- x(1) = x(0) = 0 (as d_0 = 0),
- x(2) = 2^2-1 - x(1) = 3 (as d_1 = 2),
- x(3) = x(2) = 3 (as d_2 = 1 <> 2),
- x(4) = x(3) = 3 (as d_3 = 1 <> 2),
- hence a(42) = 3.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..6560
• Wikipedia, T-square (fractal)

Crossrefs

Cf. A005836, A332497 (corresponding x's and additional comments).

Programs

PARI

a(n) = { my (y=0, k=1); while (n, if (n%3==2, y=2^k-1-y); n\=3; k++); y }

Formula

a(n) = 0 iff n belongs to A005836.