A154437 Permutation of nonnegative integers: A059893-conjugate of A154435.

0, 1, 3, 2, 5, 6, 7, 4, 13, 10, 11, 12, 9, 14, 15, 8, 21, 26, 27, 20, 25, 22, 23, 24, 29, 18, 19, 28, 17, 30, 31, 16, 53, 42, 43, 52, 41, 54, 55, 40, 45, 50, 51, 44, 49, 46, 47, 48, 37, 58, 59, 36, 57, 38, 39, 56, 61, 34, 35, 60, 33, 62, 63, 32, 85, 106, 107, 84, 105, 86, 87

Offset

0,3

Comments

This permutation is induced by the same Lamplighter group generating wreath recursion (binary transducer) as A154435, 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

From Yosu Yurramendi, Feb 23 2020: (Start)

a(n) = A054429(A284459(n)) = A258996(A153154(n)) = A284459(A065190(n)).

a(1) = 1; for n > 0, a(2*n) = 2*a(A065190(n)) + 1, a(2*n+1) = 2*a(n). (End)

Prog

(R)
maxn <- 63 # by choice
a <- c(1, 3, 2)
for(n in 2:maxn){
a[2*n+1] <- 2*a[n]
if(n%%2 == 0) a[2*n] <- 2*a[n+1] + 1
else          a[2*n] <- 2*a[n-1] + 1
}
(a <- c(0, a))
# Yosu Yurramendi, Feb 23 2020

Crossrefs

Inverse: A154438. a(n) = A059893(A154435(A059893(n))) = A054429(A153154(A054429(n))).

Sequence in context: A175058 A250090 A334999 * A305428 A269376 A257793

Adjacent sequences: A154434 A154435 A154436 * A154438 A154439 A154440

Keyword

nonn,base

Author

Antti Karttunen, Jan 17 2009

Status

approved