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

0,2

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 multiplicative walk 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

Formula

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

Prog

(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));

Crossrefs

Cf. A300839 (inverse permutation).

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

Sequence in context: A147557 A117025 A078021 * A106342 A247563 A322702

Adjacent sequences: A300835 A300836 A300837 * A300839 A300840 A300841

Keyword

nonn,base

Author

Antti Karttunen & Peter Munn, Apr 15 2018

Status

approved