Search: id:A055778
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%I A055778
%S A055778 0,1,2,2,3,3,3,2,3,4,4,5,4,4,4,5,4,4,2,3,4,4,5,5,5,4,5,6,6,7,5,5,5,6,5,
%T A055778 5,4,5,6,6,7,5,5,5,6,5,5,2,3,4,4,5,5,5,4,5,6,6,7,6,6,6,7,6,6,4,5,6,6,7,
%U A055778 7,7,6,7,8,8,9,6,6,6,7,6,6,5,6,7,7,8,6,6,6,7,6,6,4,5,6,6,7,7,7,6,7,8,8
%N A055778 Number of 1's in base phi representation of n.
%C A055778 Uses greedy algorithm (start with largest possible power of phi, then 
               work downward)
%C A055778 constant (float): phi=(sqrt(5)+1)/2; function: lphi(x)=log(x)/log(phi); 
               variable (float): rem=n; variable (integer): count=0; loop: while 
               rem>0 {rem=rem-phi^floor[lphi(x)]; count++;} result: return count;
%H A055778 R. Knott, <a href="http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/
               phigits.html">iUsing Powers of Phi to represent Integers (Base Phi)</
               a> (inspiration for this sequence).
%H A055778 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               PhiNumberSystem.html">Phi Number System</a>
%e A055778 4 in base phi is 101.01, which has three 1's.
%Y A055778 Sequence in context: A059253 A108133 A014499 this_sequence A106482 A122462 
               A165024
%Y A055778 Adjacent sequences: A055775 A055776 A055777 this_sequence A055779 A055780 
               A055781
%K A055778 base,easy,nonn
%O A055778 0,3
%A A055778 Robert Lozyniak (11(AT)onna.com), Jul 12 2000
%E A055778 More terms and algorithm from Henry Bottomley (se16(AT)btinternet.com), 
               Aug 04 2000

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