A093348 - OEIS

%I #20 Jun 17 2022 03:42:13

%S 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,

%T 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,

%U 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

%N A 5-fractal "castle" starting with 0.

%H Amiram Eldar, <a href="/A093348/b093348.txt">Table of n, a(n) for n = 1..10000</a>

%H Benoit Cloitre, <a href="https://web.archive.org/web/20050426011033/http://ns3131.ovh.net/~pi314/temporaires/benoit/chateau_pentafractal_25.JPG">Graph of a(n) for n=1 up to 25</a>

%H Benoit Cloitre, <a href="https://web.archive.org/web/20050426011033/http://ns3131.ovh.net/~pi314/temporaires/benoit/chateau_pentafractal_125.JPG">Graph of a(n) for n=1 up to 125</a>

%H Benoit Cloitre, <a href="https://web.archive.org/web/20050426011033/http://ns3131.ovh.net/~pi314/temporaires/benoit/chateau_pentafractal_625.JPG">Graph of a(n) for n=1 up to 625</a>

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

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

%F 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

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

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

%Y Cf. A093347, A093349.

%Y Cf. A060904.

%K nonn

%O 1,6

%A _Benoit Cloitre_, Apr 26 2004