A305424 Permutation of natural numbers: a(n) = A305422(2*n-1).

1, 2, 4, 3, 6, 7, 11, 8, 16, 13, 5, 22, 19, 12, 14, 25, 50, 29, 31, 28, 37, 38, 24, 41, 9, 32, 26, 47, 44, 55, 59, 10, 20, 61, 21, 118, 67, 88, 110, 53, 69, 18, 64, 73, 94, 87, 43, 52, 91, 100, 58, 97, 56, 15, 103, 62, 82, 109, 115, 48, 23, 74, 76, 49, 98, 117, 113, 152, 131, 46, 148, 137, 143, 164, 218, 27, 96, 227, 145, 230, 89, 182, 200

Offset: 1

Author

Antti Karttunen, Jun 08 2018

Keywords

• nonn

Comments

Odd bisection of A305422 and A305425.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..8191
• Index entries for sequences related to polynomials in ring GF(2)[X]
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Cf. A305423 (inverse).

Cf. A014580, A091225, A304522, A305425.

Cf. also A064216.

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); };
A305424(n) = A305422(n+n-1);

Formula

a(n) = A305422(2*n-1).