A048680 - OEIS

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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).

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 (list; graph; refs; listen; history; internal format)

	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	`R. 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));`
	CROSSREFS	`Cf. A003714, A005203, A048678, A048679.` `Equals A074049(n+1) - 1.` `Sequence in context: A035506 A006016 A054239 * A178898 A143529 A103867` `Adjacent sequences: A048677 A048678 A048679 * A048681 A048682 A048683`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen, Jul 14 1999`

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Last modified February 17 14:50 EST 2012. Contains 206050 sequences.