A305425 a(n) = n/2 for even n, a(n) = A305422(n) for odd n.

1, 1, 2, 2, 4, 3, 3, 4, 6, 5, 7, 6, 11, 7, 8, 8, 16, 9, 13, 10, 5, 11, 22, 12, 19, 13, 12, 14, 14, 15, 25, 16, 50, 17, 29, 18, 31, 19, 28, 20, 37, 21, 38, 22, 24, 23, 41, 24, 9, 25, 32, 26, 26, 27, 47, 28, 44, 29, 55, 30, 59, 31, 10, 32, 20, 33, 61, 34, 21, 35, 118, 36, 67, 37, 88, 38, 110, 39, 53, 40, 69, 41, 18, 42, 64, 43, 73, 44, 94, 45, 87, 46, 43, 47

Offset: 1

Author

Antti Karttunen, Jun 08 2018

Keywords

• nonn

Comments

Each k occurs exactly twice, at 2k and at A305421(k).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..65537
• Index entries for sequences related to polynomials in ring GF(2)[X]

Crossrefs

Bisections: A000027 and A305422.

Cf. also A252463.

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); };
A305425(n) = if(n%2,A305422(n),n/2);

Formula

a(n) = n/2 if n is even, a(n) = A305422(n) if n is odd.