A245701 Permutation of natural numbers: a(1) = 1, a(A014580(n)) = 2*a(n), a(A091242(n)) = 2*a(n)+1, where A014580(n) = binary code for n-th irreducible polynomial over GF(2), A091242(n) = binary code for n-th reducible polynomial over GF(2).

1, 2, 4, 3, 5, 9, 8, 7, 11, 19, 6, 17, 10, 15, 23, 39, 13, 35, 18, 21, 31, 47, 79, 27, 16, 71, 37, 43, 63, 95, 14, 159, 55, 33, 143, 75, 22, 87, 127, 191, 38, 29, 319, 111, 67, 287, 12, 151, 45, 175, 255, 383, 77, 59, 34, 639, 223, 135, 20, 575, 30, 25, 303, 91, 351, 511, 46, 767, 155, 119, 69, 1279, 78, 447, 271, 41, 1151, 61, 51

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..10001

Antti Karttunen, Entanglement Permutations, 2016-2017

Index entries for sequences related to polynomials in ring GF(2)[X]

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, and for n > 1, if n is in A014580, a(n) = 2*a(A091226(n)), otherwise a(n) = 1 + 2*a(A091245(n)).

As a composition of related permutations:

a(n) = A135141(A245704(n)).

Other identities:

For all n >= 1, 1 - A000035(a(n)) = A091225(n). [Maps binary representations of irreducible GF(2) polynomials (= A014580) to even numbers and the corresponding representations of reducible polynomials to odd numbers].

Prog

(PARI)
allocatemem(123456789);
A091226 = vector(2^22);
isA014580(n)=polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from Charles R Greathouse IV
n=2; while((n < 2^22), if(isA014580(n), A091226[n] = A091226[n-1]+1, A091226[n] = A091226[n-1]); n++)
A091245(n) = ((n-A091226[n])-1);
A245701(n) = if(1==n, 1, if(isA014580(n), 2*(A245701(A091226[n])), 1 + 2*(A245701(A091245(n)))));
for(n=1, 10001, write("b245701.txt", n, " ", A245701(n)));
(Scheme, with memoizing definec-macro)
(definec (A245701 n) (cond ((= 1 n) n) ((= 1 (A091225 n)) (* 2 (A245701 (A091226 n)))) (else (+ 1 (* 2 (A245701 (A091245 n)))))))

Crossrefs

Inverse: A245702.

Cf. A000035, A014580, A091242, A091225, A091226, A091245.

Similar entanglement permutations: A135141, A193231, A237427, A243287, A245703, A245704.

Sequence in context: A091451 A365389 A246161 * A082330 A082329 A072799

Adjacent sequences: A245698 A245699 A245700 * A245702 A245703 A245704

Keyword

nonn,look,hear

Author

Antti Karttunen, Aug 02 2014

Status

approved