A304529 a(1) = 0, a(2n) = n, a(2n+1) = a(A305422(2n+1)).

0, 1, 1, 2, 2, 3, 1, 4, 3, 5, 1, 6, 1, 7, 4, 8, 8, 9, 1, 10, 2, 11, 11, 12, 1, 13, 6, 14, 7, 15, 1, 16, 25, 17, 7, 18, 1, 19, 14, 20, 1, 21, 19, 22, 12, 23, 1, 24, 3, 25, 16, 26, 13, 27, 1, 28, 22, 29, 1, 30, 1, 31, 5, 32, 10, 33, 1, 34, 2, 35, 59, 36, 1, 37, 44, 38, 55, 39, 13, 40, 2, 41, 9, 42, 32, 43, 1, 44, 47, 45, 1, 46, 19, 47, 26, 48, 1, 49, 50, 50

Offset: 1

Author

Antti Karttunen, Jun 10 2018

Keywords

• nonn

Comments

This is GF(2)[X] analog of A246277.

For all i, j: a(i) = a(j) => A278233(i) = A278233(j).

For all i, j: a(i) = a(j) => A305788(i) = A305788(j).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences operating on GF(2)[X]-polynomials

Crossrefs

Cf. A305422, A305425.

Cf. A014580 (positions of 1's), A278233, A305788.

Cf. also A246277.

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); };
A304529(n) = if(1==n,0,while(n%2, n = A305422(n)); n/2);

Formula

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