Search: id:A147561
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%I A147561
%S A147561 2,3,2,2,2,3,2,2,3,5,5,3,2,2,3,2,2,3,5,5,3,2,2,3,3,4,5,5,4,3,3,2,2,3,5,
%T A147561 5,3,2,2,3,2,2,3,5,5,3,2,2,3,3,4,5,5,4,3,3,2,2,3,5,5,3,2,3,5,5,4,5,7,8,
%U A147561 5,4,5,8,7,5,4,5,5,3,2,3,5,5,3,2,2,3,3,4,5,5,4,3,3,2,2,3,5,5
%N A147561 Number of representations of n in the Fibonacci-squared base system. 
               The columns are ...,64,29,9,4,1,1 = ..8^2,5^2,3^2,2^2,1^2,1^2 i.e. 
               the Fibonacci numbers A000045 squared. The 'digits' are 0,1 or 2.
%C A147561 Note there are two columns labelled 1.
%H A147561 R. Knott, <a href="http://www.mcs.surrey.ac.uk/Personal/R.Knott/Fibonacci/
               fibrep.html#fibsqrep">Fibonacci Bases: The Fibonacci<sup>2</sup>Base 
               System</a>
%e A147561 a(2)=3 since 2 is 02, 20 and 11 using both columns labelled 1; a(10)=5 
               because 10 = 9+1 with 2 Fib-sq reps 1010,1001; 10=2x4+2 with 3 Fib-sq 
               reps 220, 211 and 202 so there are 5 Fib-sq reps for 10.
%Y A147561 Sequence in context: A097051 A078832 A086410 this_sequence A103266 A072814 
               A145390
%Y A147561 Adjacent sequences: A147558 A147559 A147560 this_sequence A147562 A147563 
               A147564
%K A147561 nonn
%O A147561 1,1
%A A147561 Ron Knott (maths(AT)ronknott.com), Nov 07 2008

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