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

1,3

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]

Formula

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

Prog

(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);

Crossrefs

Bisections: A000027 and A305422.

Cf. also A252463.

Sequence in context: A292421 A205563 A147594 * A212652 A303691 A205678

Adjacent sequences: A305422 A305423 A305424 * A305426 A305427 A305428

Keyword

nonn

Author

Antti Karttunen, Jun 08 2018

Status

approved