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

0,3

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

Formula

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

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));

Prog

(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

Crossrefs

Cf. A003714, A005203, A048678, A048679.

Equals A074049(n+1) - 1.

Sequence in context: A054239 A305424 A371590 * A342793 A178898 A296616

Adjacent sequences: A048677 A048678 A048679 * A048681 A048682 A048683

Keyword

nonn,easy

Author

Antti Karttunen, Jul 14 1999

Status

approved