A268821 Permutation of nonnegative integers: a(0) = 0, a(n) = A268717(1 + A268717(n-1)).

0, 1, 3, 2, 7, 6, 13, 12, 5, 4, 25, 24, 9, 8, 15, 14, 11, 10, 49, 48, 17, 16, 23, 22, 19, 18, 27, 26, 31, 30, 21, 20, 29, 28, 97, 96, 33, 32, 39, 38, 35, 34, 43, 42, 47, 46, 37, 36, 45, 44, 51, 50, 55, 54, 61, 60, 53, 52, 41, 40, 57, 56, 63, 62, 59, 58, 193, 192, 65, 64, 71, 70, 67, 66, 75, 74, 79, 78, 69, 68, 77, 76, 83, 82

Offset: 0

Author

Antti Karttunen, Feb 14 2016

Keywords

• nonn

Comments

The "shifted square" of permutation A268717.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..8191
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A268822.

Row 2 of array A268820.

From term a(2) onward (3, 2, 7, 6, ...) also row 3 of A268715.

Cf. A268717, A268823.

Cf. also A101080, A268833.

Programs

Mathematica

A003188[n_]:=BitXor[n, Floor[n/2]]; A006068[n_]:=If[n<2, n, Block[{m = A006068[Floor[n/2]]}, 2m + Mod[Mod[n, 2] + Mod[m, 2], 2]]]; A268717[n_]:=If[n<1, 0, A003188[1 + A006068[n - 1]]]; Table[If[n<2, n, A268717[1 + A268717[n - 1]]], {n, 0, 100}] (* Indranil Ghosh, Apr 01 2017 *)

PARI

A003188(n) = bitxor(n, n\2);
A006068(n) = if(n<2, n, {my(m = A006068(n\2)); 2*m + (n%2 + m%2)%2});
A268717(n) = if(n<1, 0, A003188(1 + A006068(n - 1)));
for(n=0, 100, print1(if(n<2, n, A268717(1 + A268717(n - 1))), ", ")) \\ Indranil Ghosh, Apr 01 2017

Python

def A003188(n): return n^(n//2)
def A006068(n):
    if n<2: return n
    else:
        m=A006068(n//2)
        return 2*m + (n%2 + m%2)%2
def A268717(n): return 0 if n<1 else A003188(1 + A006068(n - 1))
def a(n): return A268717(1 + A268717(n-1)) if n>0 else 0
print([a(n) for n in range(101)]) # Indranil Ghosh, Apr 01 2017

Scheme

(define (A268821 n) (if (zero? n) n (A268717 (+ 1 (A268717 (- n 1))))))

Formula

a(0) = 0, for n >= 1, a(n) = A268717(1 + A268717(n-1)).

Other identities. For all n >= 0:

A101080(n, a(n+2)) = 2.