A093348 A 5-fractal "castle" starting with 0.

0, 1, 0, 1, 0, 5, 4, 5, 4, 5, 0, 1, 0, 1, 0, 5, 4, 5, 4, 5, 0, 1, 0, 1, 0, 25, 24, 25, 24, 25, 20, 21, 20, 21, 20, 25, 24, 25, 24, 25, 20, 21, 20, 21, 20, 25, 24, 25, 24, 25, 0, 1, 0, 1, 0, 5, 4, 5, 4, 5, 0, 1, 0, 1, 0, 5, 4, 5, 4, 5, 0, 1, 0, 1, 0, 25, 24, 25, 24, 25, 20, 21, 20, 21, 20, 25, 24

Offset: 1

Author

Benoit Cloitre, Apr 26 2004

Keywords

• nonn

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Benoit Cloitre, Graph of a(n) for n=1 up to 25
• Benoit Cloitre, Graph of a(n) for n=1 up to 125
• Benoit Cloitre, Graph of a(n) for n=1 up to 625

Crossrefs

Cf. A093347, A093349.

Cf. A060904.

Programs

Mathematica

a[n_] := Sum[(-1)^(i+1) * 5^IntegerExponent[i, 5], {i, 1, n-1}]; Array[a, 100] (* Amiram Eldar, Jun 17 2022 *)

PARI

a(n)=if(n<2,0,5^floor(log(n-1)/log(5))-a(n-5^floor(log(n-1)/log(5))))

Formula

a(1) = 0, then a(n) = w(n) - a(n-w(n)) where w(n) = 5^floor(log(n-1)/log(5)).

a(n) = Sum_{i=1..n-1} (-1)^(i-1)*5^valuation(i, 5).

Conjecture: a(n+1) = (n mod 2) + Sum_{k=0..infinity} (4*5^k*(floor(n/5^(k+1)) mod 2)). - Charlie Neder, May 25 2019