A231551 Position of n in A231550.

0, 1, 2, 3, 4, 7, 6, 5, 8, 15, 14, 9, 12, 11, 10, 13, 16, 31, 30, 17, 28, 19, 18, 29, 24, 23, 22, 25, 20, 27, 26, 21, 32, 63, 62, 33, 60, 35, 34, 61, 56, 39, 38, 57, 36, 59, 58, 37, 48, 47, 46, 49, 44, 51, 50, 45, 40, 55, 54, 41, 52, 43, 42, 53, 64, 127, 126, 65

Offset: 0

Author

Alex Ratushnyak, Nov 10 2013

Keywords

• nonn
• easy
• look

Comments

This permutation transforms the enumeration system of positive irreducible fractions A002487/A002487' (Calkin-Wilf) into the enumeration system A020651/A020650, and A162911/A162912 (Drib) the enumeration system into A245327/A245326. - Yosu Yurramendi, Jun 16 2015

Links

• Ivan Neretin, Table of n, a(n) for n = 0..8192
• Index entries for sequences that are permutations of the nonnegative integers

Crossrefs

Cf. A003188, A006068, A231550.

Programs

Mathematica

Join[{0, 1}, Table[d = Reverse@IntegerDigits[n, 2]; FromDigits[Reverse@Append[FoldList[BitXor, d[[1]], Most@Rest@d], d[[-1]]], 2], {n, 2, 67}]] (* Ivan Neretin, Dec 28 2016 *)

Python

for n in range(99):
  bits = [0]*64
  orig = [0]*64
  l = int.bit_length(int(n))
  t = n
  for i in range(l):
    bits[i] = orig[i] = t&1
    t>>=1
  #for i in range(1, l-1):  bits[i] ^= orig[i-1]   # A231550
  for i in range(1, l-1):  bits[i] ^= bits[i-1]   # A231551
  #for i in range(l-1):  bits[i] ^= orig[i+1]      # A003188
  #for i in range(1, l):  bits[l-1-i] ^= bits[l-i]  # A006068
  t = 0
  for i in range(l):  t += bits[i]<
				

R

maxrow <- 8 # by choice
b01 <- 0 # b01 is going to be A010059
a <- 1
for(m in 0:maxrow) for(k in 0:(2^m-1)){
   b01[2^(m+1)+    k] <-     b01[2^m+k]
     a[2^(m+1)+    k] <-       a[2^m+k]  + 2^(m+b01[2^(m+1)+    k])
   b01[2^(m+1)+2^m+k] <- 1 - b01[2^m+k]
     a[2^(m+1)+2^m+k] <-       a[2^m+k]  + 2^(m+b01[2^(m+1)+2^m+k])
}
(a <- c(0,a))
# Yosu Yurramendi, Apr 10 2017

R

maxblock <- 8 # by choice
a <- 1:3
for(n in 4:2^maxblock){
ones <- which(as.integer(intToBits(n)) == 1)
nbit <- as.integer(intToBits(n))[1:tail(ones, n = 1)]
anbit <- nbit
for(i in 2:(length(anbit) - 1))
   anbit[i] <- bitwXor(anbit[i], anbit[i-1])  # ?bitwXor
a <- c(a, sum(anbit*2^(0:(length(anbit) - 1))))
}
(a <- c(0,a))
# Yosu Yurramendi, Apr 25 2021

Formula

A231550(a(n)) = a(A231550(n)) = n.

a(n) = A258996(A284460(n)) = A284459(A092569(n)), n > 0. - Yosu Yurramendi, Apr 10 2017

a(n) = A054429(A153154(n)), n > 0. - Yosu Yurramendi, Oct 04 2021