id:A048679 - OEIS Search Results

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Compressed fibbinary numbers (A003714), with rewrite 0->0, 01->1.

+0
12

0, 1, 2, 4, 3, 8, 5, 6, 16, 9, 10, 12, 7, 32, 17, 18, 20, 11, 24, 13, 14, 64, 33, 34, 36, 19, 40, 21, 22, 48, 25, 26, 28, 15, 128, 65, 66, 68, 35, 72, 37, 38, 80, 41, 42, 44, 23, 96, 49, 50, 52, 27, 56, 29, 30, 256, 129, 130, 132, 67, 136, 69, 70, 144, 73, 74, 76, 39, 160, 81 (list; graph; listen)

	OFFSET	`0,3`
	COMMENT	`Permutation of the nonnegative integers (A001477); inverse permutation of A048680 i.e. A048679[ A048680[ n ] ] = n for all n.`
	LINKS	`Index entries for sequences that are permutations of the natural numbers`
	FORMULA	`a(n) = rewrite_0to0_x1to1(fibbinary(j)) (where fibbinary(j) = A003714[ n ])` `a(n) = A106151(2*A003714(n)) for n > 0. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), May 09 2005`
	MAPLE	`rewrite_0to0_x1to1 := proc(n) option remember; if(0 = n) then RETURN(n); else RETURN((2 * rewrite_0to0_x1to1(floor(n/(2^(1+(n mod 2)))))) + (n mod 2)); fi; end;` `fastfib := n -> round((((sqrt(5)+1)/2)^n)/sqrt(5)); fibinv_appr := n -> floor(log[ (sqrt(5)+1)/2 ](sqrt(5)*n)); fibinv := n -> (fibinv_appr(n) + floor(n/fastfib(1+fibinv_appr(n)))); fibbinary := proc(n) option remember; if(n <= 2) then RETURN(n); else RETURN((2^(fibinv(n)-2))+fibbinary_seq(n-fastfib(fibinv(n)))); fi; end;`
	CROSSREFS	`Cf. A003714, A005203, A048678, A048680.` `Sequence in context: A135141 A098709 A054238 this_sequence A075378 A101905 A053211` `Adjacent sequences: A048676 A048677 A048678 this_sequence A048680 A048681 A048682`
	KEYWORD	`nonn`
	AUTHOR	`Antti Karttunen`

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Last modified November 25 20:09 EST 2009. Contains 167514 sequences.

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