A284459 Permutation of the positive integers: this permutation transforms the enumeration system of positive irreducible fractions A002487/A002487' (Calkin-Wilf) into the enumeration system A245327/A245328, and A162911/A162912 (Drib) into A020651/A020650 (Yu-Ting inverted).

1, 2, 3, 6, 5, 4, 7, 10, 13, 12, 11, 14, 9, 8, 15, 26, 21, 20, 27, 22, 25, 24, 23, 18, 29, 28, 19, 30, 17, 16, 31, 42, 53, 52, 43, 54, 41, 40, 55, 50, 45, 44, 51, 46, 49, 48, 47, 58, 37, 36, 59, 38, 57, 56, 39, 34, 61, 60, 35, 62, 33, 32, 63

Offset: 1

Author

Yosu Yurramendi, Mar 27 2017

Keywords

• nonn

Comments

The inverse permutation is A284460.

Links

• Yosu Yurramendi, Table of n, a(n) for n = 1..16383
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A002487, A020650, A020651, A162911, A162912, A245327, A245328, A284460.

Programs

R

maxrow <- 12 # by choice
a <- 1
b01 <- 1
for(m in 0:maxrow){
  b01 <- c(b01, c(1-b01[2^m:(2^(m+1)-1)], b01[2^m:(2^(m+1)-1)]) )
  for(k in 0:(2^m-1)){
    a[2^(m+1) +       k] <- a[2^m + k] + 2^(m + b01[2^(m+1) +       k])
    a[2^(m+1) + 2^m + k] <- a[2^m + k] + 2^(m + b01[2^(m+1) + 2^m + k])
}}
a
# Yosu Yurramendi, Mar 27 2017

R

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
for(i in 2:(length(anbit) - 1))
   anbit[i] <- 1 - bitwXor(anbit[i], anbit[i-1])
a <- c(a, sum(anbit*2^(0:(length(anbit) - 1))))
}
a
# Yosu Yurramendi, Apr 25 2021

Formula

a(n) = A258996(A231551(n)) = A231551(A092569(n)), n > 0 . - Yosu Yurramendi, Apr 10 2017