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%I #11 Aug 21 2014 00:00:10
%S 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,
%T 32,52,58,120,20,31,128,208,232,50,36,61,114,384,960,17,464,22,160,
%U 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
%N Permutation of natural numbers: a(n) = A246201(A193231(n)).
%C This permutation has the same cycle structure as A246163 has because this is its A193231-conjugate.
%C On the other hand, it shares with A246201 the following property:
%C 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).
%C 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.
%C See also comments at A246161 and A246163.
%H Antti Karttunen, <a href="/A246203/b246203.txt">Table of n, a(n) for n = 1..10001</a>
%H <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%H <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F a(n) = A246201(A193231(n)).
%F a(n) = A193231(A246163(A193231(n))).
%F Other identities:
%F 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].
%o (Scheme)
%o (define (A246203 n) (A246201 (A193231 n)))
%Y Inverse: A246204.
%Y Related permutations: A193231, A246201, A246161, A246163.
%Y Cf. also A000035, A091225, A246156.
%K nonn
%O 1,2
%A _Antti Karttunen_, Aug 19 2014
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