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A182578 Number of ones in Zeckendorf representation of n^n.

%I A182578 #14 Jun 15 2018 08:22:15
%S A182578 1,1,2,3,3,6,3,10,13,12,16,15,20,24,20,30,25,31,26,33,33,31,34,42,49,
%T A182578 49,53,55,56,55,58,64,64,67,73,78,70,76,77,75,89,83,92,90,106,99,100,
%U A182578 99,107,116,107,115,125,125,122,119,127,137,127,138,155,156,153,160
%N A182578 Number of ones in Zeckendorf representation of n^n.
%H A182578 Chai Wah Wu, <a href="/A182578/b182578.txt">Table of n, a(n) for n = 0..10000</a>
%e A182578 5^5 = {1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 0, 1, 0, 1, 0, 1, 0} in the Zeckendorf base.
%o A182578 (Python)
%o A182578 def A182578(n):
%o A182578     m, tlist, s = n**n, [1,2], 0
%o A182578     while tlist[-1]+tlist[-2] <= m:
%o A182578         tlist.append(tlist[-1]+tlist[-2])
%o A182578     for d in tlist[::-1]:
%o A182578         if d <= m:
%o A182578             s += 1
%o A182578             m -= d
%o A182578     return s # _Chai Wah Wu_, Jun 14 2018
%Y A182578 Cf. A007895, A020908, A020910, A025496-A025502, A182535, A182576, A182577, A000312.
%K A182578 nonn
%O A182578 0,3
%A A182578 _Alex Ratushnyak_, May 05 2012