A300838 - OEIS

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

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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));