id:A048680 - OEIS Search Results

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

+0
10

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; listen)

	OFFSET	`0,3`
	COMMENT	`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.` `Adjacent sequences: A048677 A048678 A048679 this_sequence A048681 A048682 A048683` `Sequence in context: A035506 A006016 A054239 this_sequence A143529 A103867 A075375`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen, Jul 14 1999`

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Last modified October 13 20:18 EDT 2008. Contains 145016 sequences.

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