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

Author

Antti Karttunen, Jan 17 2009

Keywords

• nonn
• base

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

Crossrefs

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

Programs

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

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)