A245702 Permutation of natural numbers: a(1) = 1, a(2n) = A014580(a(n)), a(2n+1) = A091242(a(n)), where A014580(n) = binary code for n-th irreducible polynomial over GF(2) and A091242(n) = binary code for n-th reducible polynomial over GF(2).

1, 2, 4, 3, 5, 11, 8, 7, 6, 13, 9, 47, 17, 31, 14, 25, 12, 19, 10, 59, 20, 37, 15, 319, 62, 87, 24, 185, 42, 61, 21, 137, 34, 55, 18, 97, 27, 41, 16, 415, 76, 103, 28, 229, 49, 67, 22, 3053, 373, 433, 79, 647, 108, 131, 33, 1627, 222, 283, 54, 425, 78, 109, 29, 1123, 166, 203, 45, 379, 71, 91, 26, 731, 121, 145, 36, 253, 53, 73, 23

Offset

1,2

Links

Antti Karttunen, Table of n, a(n) for n = 1..383

Index entries for sequences operating on GF(2)[X]-polynomials

Index entries for sequences that are permutations of the natural numbers

Formula

a(1) = 1, a(2n) = A014580(a(n)), a(2n+1) = A091242(a(n)).

As a composition of related permutations:

a(n) = A245703(A227413(n)).

Other identities:

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

Prog

(PARI)
allocatemem(123456789);
a014580 = vector(2^18);
a091242 = vector(2^22);
isA014580(n)=polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from Charles R Greathouse IV
i=0; j=0; n=2; while((n < 2^22), if(isA014580(n), i++; a014580[i] = n, j++; a091242[j] = n); n++)
A245702(n) = if(1==n, 1, if(0==(n%2), a014580[A245702(n/2)], a091242[A245702((n-1)/2)]));
for(n=1, 383, write("b245702.txt", n, " ", A245702(n)));
(Scheme, with memoizing definec-macro)
(definec (A245702 n) (cond ((< n 2) n) ((even? n) (A014580 (A245702 (/ n 2)))) (else (A091242 (A245702 (/ (- n 1) 2))))))

Crossrefs

Inverse: A245701.

Cf. A000035, A014580, A091242, A091225.

Similar entanglement permutations: A193231, A227413, A237126, A243288, A245703, A245704.

Sequence in context: A338161 A232799 A276472 * A297706 A093416 A073944

Adjacent sequences: A245699 A245700 A245701 * A245703 A245704 A245705

Keyword

nonn

Author

Antti Karttunen, Aug 02 2014

Status

approved