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

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, 31, 51, 32, 53, 54, 88, 13, 22, 23, 38, 24, 40, 41, 67, 26, 43, 44, 72, 45, 74, 75, 122, 29, 48, 49, 80, 50, 82, 83, 135, 52, 85, 86, 140, 87, 142, 143, 232, 21, 35, 36, 59, 37, 61

Offset: 0

Author

Antti Karttunen, Jul 14 1999

Keywords

• nonn
• easy

Comments

A permutation of the nonnegative integers (A001477). Inverse permutation to A048679, i.e. A048679[ A048680[ n ] ] = n for all n and vice versa.

Links

• Charles R Greathouse IV, Table of n, a(n) for n = 0..10000
• Ron Knott, About Fibonacci Number System
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A003714, A005203, A048678, A048679.

Equals A074049(n+1) - 1.

Programs

Maple

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));

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

Formula

a(n) = interpret_as_zeckendorf_expansion(rewrite_0to0_1to01(n)) (where rewrite_0to0_1to01(n)=A048678[ n ])