A302844 Permutation of nonnegative integers: a(n) = A003188(A163356(n)).

0, 1, 2, 3, 12, 15, 14, 13, 10, 9, 8, 11, 4, 5, 6, 7, 24, 27, 26, 25, 30, 31, 28, 29, 18, 19, 16, 17, 22, 21, 20, 23, 40, 43, 42, 41, 46, 47, 44, 45, 34, 35, 32, 33, 38, 37, 36, 39, 56, 57, 58, 59, 52, 55, 54, 53, 50, 49, 48, 51, 60, 61, 62, 63, 192, 195, 194, 193, 198, 199, 196, 197, 202, 203, 200, 201, 206, 205

Offset: 0

Author

Antti Karttunen, Apr 14 2018

Keywords

• nonn

Comments

When A207901, which is a multiplicative walk permutation, is composed from the right with this permutation, the result is A302781, another multiplicative walk permutation.

Links

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

Crossrefs

Cf. A302843 (inverse).

Cf. A003188, A006068, A057300, A163356, A302846, A302781.

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); };
A163356(n) = if(!n,n,my(i = (#binary(n)-1)\2, f = 4^i, d = (n\f)%4, r = (n%f)); (((((2+(i%2))^d)%5)-1)*f) + if(3==d,f-1-A163356(r),A057300(A163356(r)))); \\ Antti Karttunen, Apr 14 2018
A302844(n) = A003188(A163356(n));

Formula

a(n) = A003188(A163356(n)).

a(n) = A006068(A302846(n)).