A154438 Permutation of nonnegative integers: A059893-conjugate of A154436.

0, 1, 3, 2, 7, 4, 5, 6, 15, 12, 9, 10, 11, 8, 13, 14, 31, 28, 25, 26, 19, 16, 21, 22, 23, 20, 17, 18, 27, 24, 29, 30, 63, 60, 57, 58, 51, 48, 53, 54, 39, 36, 33, 34, 43, 40, 45, 46, 47, 44, 41, 42, 35, 32, 37, 38, 55, 52, 49, 50, 59, 56, 61, 62, 127, 124, 121, 122, 115, 112

Offset

0,3

Comments

This permutation is induced by the same Lamplighter group generating wreath recursion (binary transducer) as A154436, starting from the active (swapping) state a, but in contrast to it, this one rewrites the bits from the least significant end up to the second most significant bit.

Links

A. Karttunen, Table of n, a(n) for n = 0..2047

Index entries for sequences that are permutations of the natural numbers

Formula

a(0) = 0, a(1) = 1, m > 0, 0 <= k < 2^m a(2^(m+2)-1-2*k) = 2*a(2^m+k),

a(2^(m+1)+2*k) = 2*a(2^m+k) + 1. - Yosu Yurramendi, Apr 10 2020

Prog

(R)
maxlevel <- 5 # by choice
a <- 1
for(m in 0:maxlevel) for(k in 0:(2^m-1)){
  a[2^(m+2)-1-2*k] <- 2*a[2^m+k]
  a[2^(m+1)  +2*k] <- 2*a[2^m+k] + 1
}
(a <- c(0, a))
# Yosu Yurramendi, Apr 10 2020

Crossrefs

Inverse: A154437.

a(n) = A059893(A154436(A059893(n))) = A054429(A153153(A054429(n))).

Sequence in context: A153151 A175057 A153154 * A354367 A194071 A194104

Adjacent sequences: A154435 A154436 A154437 * A154439 A154440 A154441

Keyword

nonn,base

Author

Antti Karttunen, Jan 17 2009

Status

approved