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A163355
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Permutation of integers for constructing Hilbert curve in NxN grid.
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21
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0, 1, 3, 2, 14, 15, 13, 12, 4, 7, 5, 6, 8, 11, 9, 10, 16, 19, 17, 18, 20, 21, 23, 22, 30, 29, 31, 28, 24, 25, 27, 26, 58, 57, 59, 56, 54, 53, 55, 52, 60, 61, 63, 62, 50, 51, 49, 48, 32, 35, 33, 34, 36, 37, 39, 38, 46, 45, 47, 44, 40, 41, 43, 42, 234, 235, 233, 232, 236, 239
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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LINKS
| A. Karttunen, Table of n, a(n) for n = 0..262143
Index entries for sequences that are permutations of the natural numbers
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FORMULA
| a(0) = 0,
and given d=1, 2 or 3, then a((d*(4^i))+r)
= (4^i) + a(A057300(r)), if d=1 and i is even, or if d=2 and i is odd
= 2*(4^i) + a(A057300(r)), if d=3,
= 3*(4^i) + a((4^i)-1-r) in other cases.
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PROG
| (MIT Scheme:) (define (A163355 n) (let* ((i (floor->exact (/ (A000523 n) 2))) (dd (modulo (floor->exact (/ n (expt 4 i))) 4)) (r (if (zero? n) n (modulo n (expt 4 i))))) (cond ((zero? n) n) ((= 0 dd) (A163355 r)) ((= (+ 1 (modulo i 2)) dd) (+ (expt 4 i) (A163355 (A057300 r)))) ((= 3 dd) (+ (* 2 (expt 4 i)) (A163355 (A057300 r)))) (else (+ (* 3 (expt 4 i)) (A163355 (- (expt 4 i) 1 r)))))))
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CROSSREFS
| Inverse: A163356. A163357 & A163359 give two variants of Hilbert curve in NxN grid. Cf. also A163332.
Second and third "powers": A163905, A163915.
In range [A000302(n-1)..A024036(n)] of this permutation, the number of cycles is given by A163910, number of fixed points seems to be given by A147600(n-1) (fixed points themselves: A163901). Max. cycle sizes is given by A163911 and LCM's of all cycle sizes by A163912.
See also: A163890, A163894, A163902-A163903, A163914, A163485.
Sequence in context: A059374 A098384 A064536 * A145747 A055234 A204990
Adjacent sequences: A163352 A163353 A163354 * A163356 A163357 A163358
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KEYWORD
| nonn
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AUTHOR
| Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Jul 29 2009. Links to further derived sequences added Sep 21 2009.
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