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 A258746 Permutation of the positive integers: this permutation transforms the enumeration system of positive irreducible fractions A007305/A047679 (Stern-Brocot) into the enumeration system A162909/A162910 (Bird), and vice versa. 13
 1, 2, 3, 5, 4, 7, 6, 10, 11, 8, 9, 14, 15, 12, 13, 21, 20, 23, 22, 17, 16, 19, 18, 29, 28, 31, 30, 25, 24, 27, 26, 42, 43, 40, 41, 46, 47, 44, 45, 34, 35, 32, 33, 38, 39, 36, 37, 58, 59, 56, 57, 62 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS As A117120 the permutation is self-inverse. Except for fixed points 1, 2, 3 it consists completely of 2-cycles: (4,5), (6,7), (8,10), (9,11), (12,14), (13,15), (16,21), (17,20), ..., (24,29), ..., (32,42), ... . LINKS Yosu Yurramendi, Table of n, a(n) for n = 1..20001 FORMULA a(1) = 1, a(2) = 2, a(3) = 3. For n >= 2, m = floor(log_2(n)). If m even, then a(2*n) = 2*a(n) and a(2*n+1) = 2*a(n)+1. If m odd, then a(2*n) = 2*a(n)+1 and a(2*n+1) = 2*a(n). From Yosu Yurramendi, Mar 23 2017: (Start) A258996(a(n)) = a(A258996(n)) for n > 0; A117120(a(n)) = a(A117120(n)) for n > 0; A092569(a(n)) = a(A092569(n)) for n > 0; A063946(a(n)) = a(A063946(n)) for n > 0; A054429(a(n)) = a(A054429(n)) = A165199(n) for n > 0; A065190(a(n)) = a(A065190(n)) for n > 0. (End) PROG (R) a <- 1:3 maxn <- 50 # by choice # for(n in 2:maxn){   m <- floor(log2(n))   if(m%%2 == 0) {     a[2*n  ] <- 2*a[n]     a[2*n+1] <- 2*a[n]+1 }   else {     a[2*n  ] <- 2*a[n]+1     a[2*n+1] <- 2*a[n]   } } # a # Yosu Yurramendi, Jun 09 2015 (R) # Given n, compute a(n) by taking into account the binary representation of n maxblock <- 7 # by choice a <- 1:3 for(n in 4:2^maxblock){   ones <- which(as.integer(intToBits(n)) == 1) nbit <- as.integer(intToBits(n))[1:tail(ones, n = 1)] anbit <- nbit ifelse(floor(log2(n)) %% 2 == 0,    anbit[seq(1, length(anbit)-1, 2)] <- 1 - anbit[seq(1, length(anbit)-1, 2)],    anbit[seq(2, length(anbit) - 1, 2)] <- 1 - anbit[seq(2, length(anbit)-1, 2)]) a <- c(a, sum(anbit*2^(0:(length(anbit)-1)))) } a # Yosu Yurramendi, May 29 2021 CROSSREFS Cf. A117120. Sequence in context: A261102 A101212 A232641 * A064706 A100282 A100281 Adjacent sequences:  A258743 A258744 A258745 * A258747 A258748 A258749 KEYWORD nonn,changed AUTHOR Yosu Yurramendi, Jun 09 2015 STATUS approved

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Last modified June 24 06:16 EDT 2021. Contains 345416 sequences. (Running on oeis4.)