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A258996
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Permutation of the positive integers: this permutation transforms the enumeration system of positive irreducible fractions A002487/A002487' (Calkin-Wilf) into the enumeration system A162911/A162912 (Drib), and vice versa.
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20
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1, 2, 3, 6, 7, 4, 5, 10, 11, 8, 9, 14, 15, 12, 13, 26, 27, 24, 25, 30, 31, 28, 29, 18, 19, 16, 17, 22, 23, 20, 21, 42, 43, 40, 41, 46, 47, 44, 45, 34, 35, 32, 33, 38, 39, 36, 37, 58, 59, 56, 57, 62, 63, 60, 61, 50, 51, 48, 49, 54, 55, 52, 53
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OFFSET
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1,2
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COMMENTS
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AsA258746 the permutation is self-inverse. Except for fixed points 1, 2, 3 it consists completely of 2-cycles: (4,6), (5,7), (8,10), (9,11), (12,14), (13,15), (16,26), (17,27), ..., (21,31), ..., (32,42), ... . - Yosu Yurramendi, Mar 31 2016
When terms of sequence |n - a(n)|/2 (n >3) are considered only once, and they are sorted in increasing order, A147992 is obtained. - Yosu Yurramendi, Apr 05 2016
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LINKS
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FORMULA
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a(1) = 1, a(2) = 2, a(3) = 3. For n = 2^m + k, m > 1, 0 <= k < 2^m. If m is even, then a(2^(m+1)+k) = a(2^m + k) + 2^m and a(2^(m+1) + 2^m+k) = a(2^m+k) + 2^(m+1). If m is odd, then a(2^(m+1) + k) = a(2^m+k) + 2^(m+1) and a(2^(m+1) + 2^m+k) = a(2^m+k) + 2^m.
a(1) = 1, for m >= 0 and 0 <= k < 2^m, a(2^(m+1) + 2*k) = 2*a(2^(m+1) - 1 - k), a(2^(m+1) + 2*k + 1) = 2*a(2^(m+1) - 1 - k) + 1. - Yosu Yurramendi, May 23 2020
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PROG
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(R)
maxlevel <- 5 # by choice
a <- 1
for(m in 0:maxlevel) for(k in 0:(2^m-1)){
a[2^(m+1) + 2*k ] = 2*a[2^(m+1) - 1 - k]
a[2^(m+1) + 2*k + 1] = 2*a[2^(m+1) - 1 - k] + 1}
a
(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
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
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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