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A154437
Permutation of nonnegative integers: A059893-conjugate of A154435.
5
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.
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
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Jan 17 2009
STATUS
approved