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

1,6

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

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

Mathematica

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

Prog

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

Crossrefs

Cf. A093347, A093349.

Cf. A060904.

Sequence in context: A237577 A131369 A122219 * A262604 A276500 A246060

Adjacent sequences: A093345 A093346 A093347 * A093349 A093350 A093351

Keyword

nonn

Author

Benoit Cloitre, Apr 26 2004

Status

approved