A153153 Permutation of natural numbers: A059893-conjugate of A003188.

0, 1, 3, 2, 5, 6, 7, 4, 9, 10, 15, 12, 13, 14, 11, 8, 17, 18, 23, 20, 29, 30, 27, 24, 25, 26, 31, 28, 21, 22, 19, 16, 33, 34, 39, 36, 45, 46, 43, 40, 57, 58, 63, 60, 53, 54, 51, 48, 49, 50, 55, 52, 61, 62, 59, 56, 41, 42, 47, 44, 37, 38, 35, 32, 65, 66, 71, 68, 77, 78, 75, 72

Offset: 0

Author

Antti Karttunen, Dec 20 2008

Keywords

• nonn
• base

Links

• Antti Karttunen, Table of n, a(n) for n = 0..2047
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A153154. a(n) = A059893(A003188(A059893(n))).

Programs

R

a <- 1
maxlevel <- 5 # by choice
#
for(m in 0:maxlevel) for(k in 0:(2^m-1)){
  a[2^(m+1)+2*k  ] <- 2*a[2^(m+1)-1-k] + 1
  a[2^(m+1)+2*k+1] <- 2*a[2^m+k]
}
a <- c(0,a)
# Yosu Yurramendi, Jan 25 2020

Formula

a(n) = A065190(A231550(n)). - Yosu Yurramendi, Jan 15 2020

a(1) = 1, a(2^(m+1)+2*k) = 2*a(2^(m+1)-1-k), a(2^(m+1)+2*k+1) = 2*a(2^m+k), m >= 0, 0 <= k < 2^m. - Yosu Yurramendi, Jan 25 2020