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%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
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