A305423 Permutation of natural numbers: a(n) = (A305421(n)+1)/2.

1, 2, 4, 3, 11, 5, 6, 8, 25, 32, 7, 14, 10, 15, 54, 9, 137, 42, 13, 33, 35, 12, 61, 23, 16, 27, 76, 20, 18, 95, 19, 26, 126, 410, 87, 123, 21, 22, 117, 98, 24, 104, 47, 29, 499, 70, 28, 60, 64, 17, 956, 48, 40, 221, 30, 53, 184, 51, 31, 228, 34, 56, 238, 43, 641, 135, 37, 683, 41, 252, 229, 144, 44, 62, 775, 63, 90, 158, 109, 163, 131, 57

Offset: 1

Author

Antti Karttunen, Jun 08 2018

Keywords

• nonn

Links

• Antti Karttunen, Table of n, a(n) for n = 1..13106
• 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. A305424 (inverse).

Cf. A014580, A091225, A304521.

Cf. also A048673.

Programs

PARI

A091225(n) = polisirreducible(Pol(binary(n))*Mod(1, 2));
A305420(n) = { my(k=1+n); while(!A091225(k),k++); (k); };
A305421(n) = { my(f = subst(lift(factor(Pol(binary(n))*Mod(1, 2))),x,2)); for(i=1,#f~,f[i,1] = Pol(binary(A305420(f[i,1])))); fromdigits(Vec(factorback(f))%2,2); };
A305423(n) = ((1+A305421(n))/2);

Formula

a(n) = (A305421(n)+1)/2.