A305428 Permutation of nonnegative integers: a(1) = 0, a(2) = 1, a(2n) = 2*a(n), a(2n+1) = 1 + 2*a(A305422(2n+1)).

0, 1, 3, 2, 5, 6, 7, 4, 13, 10, 15, 12, 31, 14, 9, 8, 17, 26, 63, 20, 11, 30, 61, 24, 127, 62, 25, 28, 29, 18, 255, 16, 509, 34, 59, 52, 511, 126, 57, 40, 1023, 22, 253, 60, 49, 122, 2047, 48, 27, 254, 33, 124, 125, 50, 4095, 56, 121, 58, 8191, 36, 16383, 510, 21, 32, 41, 1018, 32767, 68, 23, 118, 32765, 104, 65535, 1022, 241, 252, 16381, 114, 251, 80, 47

Offset: 1

Author

Antti Karttunen, Jun 10 2018

Keywords

• nonn

Comments

Note the indexing: the domain starts from 1, while the range includes also zero.

This is GF(2)[X] analog of A243071.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..2048
• Index entries for sequences operating on GF(2)[X]-polynomials
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A305427 (inverse).

Cf. A305422.

Cf. also A243071, A305418.

Programs

PARI

A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));
A305419(n) = if(n<3,1, my(k=n-1); while(k>1 && !A091225(k),k--); (k));
A305422(n) = { my(f = subst(lift(factor(Pol(binary(n))*Mod(1, 2))),x,2)); for(i=1,#f~,f[i,1] = Pol(binary(A305419(f[i,1])))); fromdigits(Vec(factorback(f))%2,2); };
A305428(n) = if(n<=2,(n-1),if(!(n%2),2*A305428(n/2),1+(2*(A305428(A305422(n))))));

Formula

a(1) = 0, a(2) = 1, a(2n) = 2*a(n), a(2n+1) = 1 + 2*a(A305422(2n+1)).

a(n) = A054429(A305418(n)).