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A048678
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Binary expansion of nonnegative integers expanded to "Zeckendorffian format" with rewrite rules 0->0, 1->01.
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7
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0, 1, 2, 5, 4, 9, 10, 21, 8, 17, 18, 37, 20, 41, 42, 85, 16, 33, 34, 69, 36, 73, 74, 149, 40, 81, 82, 165, 84, 169, 170, 341, 32, 65, 66, 133, 68, 137, 138, 277, 72, 145, 146, 293, 148, 297, 298, 597, 80, 161, 162, 325, 164, 329, 330, 661, 168, 337, 338, 677, 340
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| No two adjacent 1-bits. Permutation of A003714.
Replace 1 with 01 in binary. - Ralf Stephan (ralf(AT)ark.in-berlin.de), 0ct 07 2003
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LINKS
| N. J. A. Sloane, Transforms
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FORMULA
| a(n) = rewrite_0to0_1to01(n) [ Each 0->1, 1->10 in binary expansion of n ]
a(0)=0; a(n)=(3-(-1)^n)*a(floor(n/2))+(1-(-1)^n)/2. - Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 31 2003
a(0)=0, a(2n) = 2a(n), a(2n+1) = 4a(n) + 1. - Ralf Stephan (ralf(AT)ark.in-berlin.de), 0ct 07 2003
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EXAMPLE
| 11=1011 in binary, thus is rewritten as 100101 = 37 in decimal.
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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;
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MATHEMATICA
| f[n_] := FromDigits[ Flatten[IntegerDigits[n, 2] /. {1 -> {0, 1}}], 2]; Table[f@n, {n, 0, 60}] [From Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 11 2009]
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PROG
| (PARI) a(n)=if(n<1, 0, (3-(-1)^n)*a(floor(n/2))+(1-(-1)^n)/2)
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CROSSREFS
| A005203, A048679, A048680.
MASKTRANS transform of A053644.
Cf. A084471, A088697, A088698.
Sequence in context: A204923 A123302 A120119 * A084432 A071297 A114393
Adjacent sequences: A048675 A048676 A048677 * A048679 A048680 A048681
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen
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