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 A165199 a(0) = 0, and for n>=1, let b(n,m) be the m-th digit, reading left to right, of binary n. (b(n, 1) is the most significant binary digit, which is 1.) Then a(n) is such that b(a(n),1)=1; and if b(n,m)=b(n,m-1) then b(a(n),m) does not = b(a(n),m-1); and if b(n,m) does not = b(n,m-1) then b(a(n), m) = b(a(n),m-1), for all m where 2 <= m <= number binary digits in n. 5
 0, 1, 3, 2, 6, 7, 4, 5, 13, 12, 15, 14, 9, 8, 11, 10, 26, 27, 24, 25, 30, 31, 28, 29, 18, 19, 16, 17, 22, 23, 20, 21, 53, 52, 55, 54, 49, 48, 51, 50, 61, 60, 63, 62, 57, 56, 59, 58, 37, 36, 39, 38, 33, 32, 35, 34, 45, 44, 47, 46, 41, 40, 43, 42, 106, 107, 104, 105, 110, 111, 108 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS This is a self-inverse permutation of the positive integers. LINKS Antti Karttunen, Table of n, a(n) for n = 0..1023 FORMULA From Antti Karttunen, Jul 22 2014: (Start) a(0) = 0, and for n >= 1, a(n) = 2*a(floor(n/2)) + A000035(n+A000523(n)). As a composition of related permutations: a(n) = A056539(A129594(n)) = A129594(A056539(n)). a(n) = A245443(A193231(n)) = A193231(A245444(n)). a(n) = A075158(A243353(n)-1) = A075158((A241909(1+A075157(n))) - 1). (End) a(n) = A258746(A054429(n)) = A054429(A258746(n)), n > 0. - Yosu Yurramendi, Mar 29 2017 EXAMPLE 12 in binary is 1100. Generating a(12): the leftmost binary digit is 1. In 1100, the 2nd digit from the left equals the first, so the second digit from the left of binary a(12) does not equal the first; so we have 10 as the two leftmost digits in binary a(12). The third digit from the left of binary 12 does not equal the second, so the third digit from the left of binary a(12) equals the second; therefore the leftmost 3 digits of a(12) in binary are 100. And finally, the rightmost digit of binary 12 equals the 3rd from the left, so the rightmost digit of binary a(12) does not equal the 3rd from the left of binary a(12). Therefore a(12) in binary is 1001. And a(12) is the decimal equivalent of this, which is 9. PROG (Scheme, with memoizing definec-macro) (definec (A165199 n) (if (zero? n) n (+ (* 2 (A165199 (floor->exact (/ n 2)))) (A000035 (+ (A000523 n) n))))) ;; Antti Karttunen, Jul 22 2014 (R) maxrow <- 8 # by choice a <- 1 for(m in 0: maxrow) for(k in 0:(2^m-1)){ a[2^(m+1) +       k] = a[2^(m+1) - 1 - k] + 2^(m+1) a[2^(m+1) + 2^m + k] = a[2^(m+1) - 1 - k] + 2^m } (a <- c(0, a)) # Yosu Yurramendi, Apr 04 2017 CROSSREFS Cf. A000035, A000523, A075157, A075158, A241909, A243353, A245443, A245444. {A001477, A129594, A165199, A056539} form a 4-group. Sequence in context: A154446 A154442 A154445 * A268825 A245812 A268826 Adjacent sequences:  A165196 A165197 A165198 * A165200 A165201 A165202 KEYWORD base,nonn,look AUTHOR Leroy Quet, Sep 07 2009 EXTENSIONS Extended by Ray Chandler, Sep 10 2009 a(0) = 0 prepended by Antti Karttunen, Jul 22 2014 STATUS approved

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Last modified January 21 11:21 EST 2019. Contains 319354 sequences. (Running on oeis4.)