A093347 A 3-fractal "castle" starting with 0.

0, 1, 0, 3, 2, 3, 0, 1, 0, 9, 8, 9, 6, 7, 6, 9, 8, 9, 0, 1, 0, 3, 2, 3, 0, 1, 0, 27, 26, 27, 24, 25, 24, 27, 26, 27, 18, 19, 18, 21, 20, 21, 18, 19, 18, 27, 26, 27, 24, 25, 24, 27, 26, 27, 0, 1, 0, 3, 2, 3, 0, 1, 0, 9, 8, 9, 6, 7, 6, 9, 8, 9, 0, 1, 0, 3, 2, 3, 0, 1, 0, 81, 80, 81, 78, 79, 78, 81

Offset

1,4

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Benoit Cloitre, Graph of a(n) for n=1 up to 9

Benoit Cloitre, Graph of a(n) for n=1 up to 27

Benoit Cloitre, Graph of a(n) for n=1 up to 81

Benoit Cloitre, Graph of a(n) for n=1 up to 243

Formula

a(1) = 0 then a(n) = w(n) - a(n-w(n)) where w(n) = 3^floor(log(n-1)/log(3)).

a(3^n) = 0, a(3^n+1) = 3^n, a(3^n+2) = 3^n-1, a(3^n+3) = 3^n, etc.

a(n) = Sum_{i=1..n-1} (-1)^(i-1)*3^valuation(i, 3).

Mathematica

a[n_] := Sum[(-1)^(i+1) * 3^IntegerExponent[i, 3], {i, 1, n-1}]; Array[a, 100] (* Amiram Eldar, Jun 17 2022 *)

Prog

(PARI) a(n)=if(n<2, 0, 3^floor(log(n-1)/log(3))-a(n-3^floor(log(n-1)/log(3))))
(PARI) a(n) = my(s=-1); fromdigits([if(d==1, s=-s) |d<-digits(n-1, 3)], 3); \\ Kevin Ryde, Jan 01 2024

Crossrefs

Cf. A093348, A093349

Cf. A038500.

Sequence in context: A325142 A047160 A332497 * A230409 A244543 A283979

Adjacent sequences: A093344 A093345 A093346 * A093348 A093349 A093350

Keyword

nonn,easy

Author

Benoit Cloitre, Apr 26 2004

Status

approved