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A066194 A permutation of the integers (a fractal sequence): a(n) = A006068(n-1) + 1. 6
1, 2, 4, 3, 8, 7, 5, 6, 16, 15, 13, 14, 9, 10, 12, 11, 32, 31, 29, 30, 25, 26, 28, 27, 17, 18, 20, 19, 24, 23, 21, 22, 64, 63, 61, 62, 57, 58, 60, 59, 49, 50, 52, 51, 56, 55, 53, 54, 33, 34, 36, 35, 40, 39, 37, 38, 48, 47, 45, 46, 41, 42, 44, 43, 128, 127, 125, 126, 121, 122 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

With an initial zero, inverse of the Gray Code (A003188). See also A006068. - Robert G. Wilson v, Jun 22 2014

I suspect the above comment refers to function A105081(n) = 1 + A003188(n - 1), n >= 1. - Antti Karttunen, Feb 15 2016

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..8192 (first 1024 terms from Robert G. Wilson v)

Index entries for sequences that are permutations of the natural numbers

FORMULA

a(n) = A006068(n-1) + 1, n >= 1. - Philippe Deléham, Apr 29 2005

a(n) = A006068(A268717(n)), composition of related permutations. - Antti Karttunen, Feb 14 2016

a(n) = 1 + Sum_{j=1..n-1} (1/6)*(-3 + (-1)^A007814(j) + 2^(A007814(j) + 3))*(-1)^(A000120(j) + 1). - John Erickson, Oct 18 2018

EXAMPLE

Third nesting gives {1,2,4,3, 8,7,5,6} by means of joining the lists {1,2,4,3} = second nesting and {8,7,6,5} permuted by {1,2,4,3} giving {8,7,5,6}.

MATHEMATICA

Nest[ Join[ #, (Length[ #] + Range[ Length[ #], 1, -1 ])[[ # ]]] &, {1}, 7 ]

GrayCode[n_] := BitXor[n, Floor[n/2]]; t = Array[ GrayCode, 1000, 0]; Table[ Position[ t, n], {n, 0, 100}] // Flatten (* Robert G. Wilson v, Jun 22 2014 *)

PROG

(Scheme) (define (A066194 n) (+ 1 (A006068 (- n 1)))) ;; Antti Karttunen, Feb 14 2016

CROSSREFS

Inverse: A105081.

Cf. A003188, A006068, A268717.

Sequence in context: A101468 A188866 A235486 * A101283 A243496 A125566

Adjacent sequences:  A066191 A066192 A066193 * A066195 A066196 A066197

KEYWORD

easy,nonn

AUTHOR

Wouter Meeussen, Dec 15 2001

EXTENSIONS

Deléham's formula added to the name by Antti Karttunen, Feb 14 2016

STATUS

approved

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Last modified March 30 19:12 EDT 2020. Contains 333127 sequences. (Running on oeis4.)