A300838 Permutation of nonnegative integers: a(n) = A057300(A003188(n)).

0, 2, 3, 1, 9, 11, 10, 8, 12, 14, 15, 13, 5, 7, 6, 4, 36, 38, 39, 37, 45, 47, 46, 44, 40, 42, 43, 41, 33, 35, 34, 32, 48, 50, 51, 49, 57, 59, 58, 56, 60, 62, 63, 61, 53, 55, 54, 52, 20, 22, 23, 21, 29, 31, 30, 28, 24, 26, 27, 25, 17, 19, 18, 16, 144, 146, 147, 145, 153, 155, 154, 152, 156, 158, 159, 157, 149, 151

Offset: 0

Author

Antti Karttunen and Peter Munn, Apr 15 2018

Keywords

• nonn
• base
• easy

Comments

Like in binary Gray code A003188, also in this permutation the binary expansions of a(n) and a(n+1) differ always by just a single bit-position, that is, A000120(A003987(a(n),a(n+1))) = 1 for all n >= 0. Here A003987 computes bitwise-XOR of its two arguments. This is true for any composition P(A003188(n)), where P is a permutation that permutes the bit-positions of binary expansion of n in some way.

When composed with A052330 this gives a divisor-or-multiple permutation similar to A207901 and A302781.

Links

• Antti Karttunen, Table of n, a(n) for n = 0..16383
• Index entries for sequences related to binary expansion of n
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A300839 (inverse permutation).

Cf. also A003188, A163252, A302846 for other permutations satisfying the same condition.

Programs

PARI

A003188(n) = bitxor(n, n>>1);
A057300(n) = { my(t=1, s=0); while(n>0,  if(1==(n%4),n++,if(2==(n%4),n--)); s += (n%4)*t; n >>= 2; t <<= 2); (s); };
A300838(n) = A057300(A003188(n));

Formula

a(n) = A057300(A003188(n)).