A231550 Permutation of nonnegative integers: for each bit[i] in the binary representation, except the most and the least significant bits, set bit[i] = bit[i] XOR bit[i-1], where bit[i-1] is the less significant bit, XOR is the binary logical exclusive or operator.

0, 1, 2, 3, 4, 7, 6, 5, 8, 11, 14, 13, 12, 15, 10, 9, 16, 19, 22, 21, 28, 31, 26, 25, 24, 27, 30, 29, 20, 23, 18, 17, 32, 35, 38, 37, 44, 47, 42, 41, 56, 59, 62, 61, 52, 55, 50, 49, 48, 51, 54, 53, 60, 63, 58, 57, 40, 43, 46, 45, 36, 39, 34, 33, 64, 67, 70, 69, 76

Offset

0,3

Comments

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

Formula

a(A231551(n)) = A231551(a(n)) = n.

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

Mathematica

Join[{0, 1}, Table[d = IntegerDigits[n, 2]; FromDigits[Join[{d[[1]]}, BitXor[Most@Rest@d, Rest@Rest@d], {d[[-1]]}], 2], {n, 2, 68}]] (* Ivan Neretin, Dec 28 2016 *)

Prog

(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]<<i
  print(str(t), end=', ')
(R)
a <- 1
maxlevel <- 8 # by choice
#
for(m in 0:maxlevel) for(k in 0:(2^m-1)){
  a[2^(m+1)  +2*k] <- 2*a[2^m+k]
  a[2^(m+2)-1-2*k] <- 2*a[2^m+k] + 1
}
(a <- c(0, a))
# Yosu Yurramendi, Apr 10 2017
(PARI) a(n) = bitxor(n, if(n>3, bitand(n<<1, bitneg(0, logint(n, 2))))); \\ Kevin Ryde, Jul 17 2021

Crossrefs

Cf. A003188, A006068, A231551.

Sequence in context: A326316 A361444 A305417 * A106453 A122199 A270196

Adjacent sequences: A231547 A231548 A231549 * A231551 A231552 A231553

Keyword

nonn,look,base,easy

Author

Alex Ratushnyak, Nov 10 2013

Status

approved