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

Author

Benoit Cloitre, Apr 26 2004

Keywords

• nonn
• easy

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

Crossrefs

Cf. A093348, A093349

Cf. A038500.

Programs

Mathematica

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

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

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).