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

0,7

Links

Rémy Sigrist, Table of n, a(n) for n = 0..6560

Wikipedia, T-square (fractal)

Formula

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

Example

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.

Prog

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

Crossrefs

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

Sequence in context: A271082 A053375 A117252 * A181407 A114187 A016037

Adjacent sequences: A332495 A332496 A332497 * A332499 A332500 A332501

Keyword

nonn,base

Author

Rémy Sigrist, Feb 14 2020

Status

approved