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Search: id:A154447
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| A154447 |
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Permutation of non-negative integers induced by wreath recursion a=s(b,c), b=s(c,a), c=(c,c), starting from state b, rewriting bits from the second most significant bit toward the least significant end. |
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+0
3
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| 0, 1, 3, 2, 6, 7, 5, 4, 12, 13, 14, 15, 11, 10, 8, 9, 24, 25, 26, 27, 28, 29, 30, 31, 22, 23, 21, 20, 16, 17, 18, 19, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 44, 45, 46, 47, 43, 42, 40, 41, 32, 33, 34, 35, 36, 37, 38, 39, 96, 97, 98, 99, 100, 101, 102
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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This permutation of natural numbers is induced by the second generator of group 2861 mentioned on page 144 of "Classification of groups generated by 3-state automata over a 2-letter alphabet" paper. It can be computed by starting scanning n's binary expansion rightward from the second most significant bit, complementing every bit down to and including A) either the first 0-bit at odd distance from the most significant bit or B) the first 1-bit at even distance from the most significant bit.
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LINKS
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A. Karttunen, Table of n, a(n) for n = 0..2047
Bondarenko, Grigorchuk, Kravchenko, Muntyan, Nekrashevych, Savchuk, Sunic, Classification of groups generated by 3-state automata over a 2-letter alphabet, p. 144.
Index entries for sequences that are permutations of the natural numbers
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EXAMPLE
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25 = 11001 in binary, the first zero-bit at odd distance from the msb is at position 1 (distance 3) and the first one-bit at even distance from the msb is at position 0 (distance 4), thus we stop at the former, after complementing the bits 3-1, which gives us 10111 (23 in binary), thus a(25)=23.
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PROGRAM
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(MIT Scheme:) (define (A154447 n) (if (< n 2) n (let loop ((maskbit (A072376 n)) (p 0) (z n)) (cond ((zero? maskbit) z) ((= p (modulo (floor->exact (/ n maskbit)) 2)) (+ z (* (- 1 (* 2 p)) maskbit))) (else (loop (floor->exact (/ maskbit 2)) (- 1 p) (- z (* (- 1 (* 2 p)) maskbit))))))))
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CROSSREFS
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Inverse: A154448. a(n) = A054429(A154448(A054429(n))). Cf. A072376, A153141-A153142, A154435-A154436, A154439-A154446. Corresponds to A154457 in the group of Catalan bijections.
Sequence in context: A120231 A083362 A153142 this_sequence A003188 A154435 A006042
Adjacent sequences: A154444 A154445 A154446 this_sequence A154448 A154449 A154450
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KEYWORD
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nonn,base
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AUTHOR
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Antti Karttunen (His-Firstname.His-Surname(AT)gmail.com), Jan 17 2009
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