A246203 Permutation of natural numbers: a(n) = A246201(A193231(n)).

1, 7, 3, 6, 2, 14, 15, 24, 8, 30, 13, 28, 5, 12, 4, 10, 56, 60, 29, 26, 16, 112, 48, 96, 9, 32, 52, 58, 120, 20, 31, 128, 208, 232, 50, 36, 61, 114, 384, 960, 17, 464, 22, 160, 896, 248, 27, 62, 240, 40, 224, 64, 104, 116, 25, 124, 80, 480, 11, 192, 57, 448, 18, 1536, 98, 456, 21, 928, 200, 512, 832, 3584, 121, 244, 144

Offset: 1

Author

Antti Karttunen, Aug 19 2014

Keywords

• nonn

Comments

This permutation has the same cycle structure as A246163 has because this is its A193231-conjugate.

On the other hand, it shares with A246201 the following property:

Because 2 is the only even term in A014580, it implies that, apart from a(2)=7, odd numbers occur in odd positions only (along with many even numbers that also occur in odd positions).

Note that for any value k in A246156, "Odd reducible polynomials over GF(2)": 5, 9, 15, 17, 21, 23, ..., a(k) will be even, and apart from 2, all other even numbers are mapped to some even number, so all those terms reside in infinite cycles, and apart from 5 and 15, all of them reside in separate cycles. The infinite cycle containing 5 and 15 goes as: ..., 14523, 3889, 103, 59, 11, 13, 5, 2, 7, 15, 4, 6, 14, 12, 28, 58, 480, 3728, 3932416, ... and it is only because a(2) = 7, that it can temporarily switch back from even terms to odd terms, until right after a(15) = 4 it is finally doomed to the eternal evenness.

See also comments at A246161 and A246163.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..10001
• Index entries for sequences operating on GF(2)[X]-polynomials
• Index entries for sequences that are permutations of the natural numbers

Crossrefs

Inverse: A246204.

Related permutations: A193231, A246201, A246161, A246163.

Cf. also A000035, A091225, A246156.

Programs

Scheme

(define (A246203 n) (A246201 (A193231 n)))

Formula

a(n) = A246201(A193231(n)).

a(n) = A193231(A246163(A193231(n))).

Other identities:

For all n > 1, A000035(a(n)) = A091225(n). [After 1 maps binary representations of reducible GF(2) polynomials to even numbers and the corresponding representations of irreducible polynomials to odd numbers, in some order].