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A048680 Nonnegative integers A001477 expanded with rewrite 0->0, 01->1, then interpreted as Zeckendorffian expansions (as numbers of Fibonacci number system).

%I A048680 #16 Jul 07 2016 23:54:46
%S A048680 0,1,2,4,3,6,7,12,5,9,10,17,11,19,20,33,8,14,15,25,16,27,28,46,18,30,
%T A048680 31,51,32,53,54,88,13,22,23,38,24,40,41,67,26,43,44,72,45,74,75,122,
%U A048680 29,48,49,80,50,82,83,135,52,85,86,140,87,142,143,232,21,35,36,59,37,61
%N A048680 Nonnegative integers A001477 expanded with rewrite 0->0, 01->1, then interpreted as Zeckendorffian expansions (as numbers of Fibonacci number system).
%C A048680 A permutation of the nonnegative integers (A001477). Inverse permutation to A048679, i.e. A048679[ A048680[ n ] ] = n for all n and vice versa.
%H A048680 Charles R Greathouse IV, <a href="/A048680/b048680.txt">Table of n, a(n) for n = 0..10000</a>
%H A048680 Ron Knott, <a href="http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/fibrep.html">About Fibonacci Number System</a>
%H A048680 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A048680 a(n) = interpret_as_zeckendorf_expansion(rewrite_0to0_1to01(n)) (where rewrite_0to0_1to01(n)=A048678[ n ])
%p A048680 rewrite_0to0_1to01 := proc(n) option remember; if(n < 2) then RETURN(n); else RETURN(((2^(1+(n mod 2))) * rewrite_0to0_1to01(floor(n/2))) + (n mod 2)); fi; end; interpret_as_zeckendorf_expansion := n -> sum('(bit_i(n,i)*fib(i+2))','i'=0..floor_log_2(n));
%o A048680 (PARI) a(n)=my(k=1,s);while(n,if(n%2,s+=fibonacci(k++));k++;n>>=1);s \\ _Charles R Greathouse IV_, Nov 17 2013
%Y A048680 Cf. A003714, A005203, A048678, A048679.
%Y A048680 Equals A074049(n+1) - 1.
%K A048680 nonn,easy
%O A048680 0,3
%A A048680 _Antti Karttunen_, Jul 14 1999