

A154447


Permutation of nonnegative 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.


3



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
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OFFSET

0,3


COMMENTS

This permutation of natural numbers is induced by the second generator of group 2861 mentioned on page 144 of "Classification of groups generated by 3state automata over a 2letter 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 0bit at odd distance from the most significant bit or B) the first 1bit at even distance from the most significant bit.


LINKS

A. Karttunen, Table of n, a(n) for n = 0..2047
Bondarenko, Grigorchuk, Kravchenko, Muntyan, Nekrashevych, Savchuk, Sunic, Classification of groups generated by 3state automata over a 2letter alphabet, p. 144.
Index entries for sequences that are permutations of the natural numbers


EXAMPLE

25 = 11001 in binary, the first zerobit at odd distance from the msb is at position 1 (distance 3) and the first onebit at even distance from the msb is at position 0 (distance 4), thus we stop at the former, after complementing the bits 31, which gives us 10111 (23 in binary), thus a(25)=23.


PROG

(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))))))))


CROSSREFS

Inverse: A154448. a(n) = A054429(A154448(A054429(n))). Cf. A072376, A153141A153142, A154435A154436, A154439A154446. Corresponds to A154457 in the group of Catalan bijections.
Sequence in context: A276442 A233275 A153142 * A003188 A269401 A268933
Adjacent sequences: A154444 A154445 A154446 * A154448 A154449 A154450


KEYWORD

nonn,base


AUTHOR

Antti Karttunen, Jan 17 2009


STATUS

approved



