This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A246202 #24 Jul 27 2015 22:11:32
%S A246202 1,4,2,8,11,5,3,14,31,17,47,9,13,6,7,21,61,42,185,24,87,62,319,15,37,
%T A246202 20,59,10,19,12,25,29,109,78,425,54,283,222,1627,33,131,108,647,79,
%U A246202 433,373,3053,22,67,49,229,28,103,76,415,16,41,27,97,18,55,34,137,39,167,134,859,98,563,494,4225,70,375,331,2705,264,2011,1832,19891,44
%N A246202 Permutation of natural numbers: a(1) = 1, a(2n) = A091242(a(n)), a(2n+1) = A014580(a(n)), where A091242(n) = binary code for n-th reducible polynomial over GF(2) and A014580(n) = binary code for n-th irreducible polynomial over GF(2).
%C A246202 This sequence can be represented as a binary tree. Each left hand child is produced as A091242(n), and each right hand child as A014580(n), when the parent contains n:
%C A246202 |
%C A246202 ...................1...................
%C A246202 4 2
%C A246202 8......../ \.......11 5......../ \........3
%C A246202 / \ / \ / \ / \
%C A246202 / \ / \ / \ / \
%C A246202 / \ / \ / \ / \
%C A246202 14 31 17 47 9 13 6 7
%C A246202 21 61 42 185 24 87 62 319 15 37 20 59 10 19 12 25
%C A246202 etc.
%C A246202 Because 2 is the only even term in A014580, it implies that, apart from a(3)=2, all other odd positions contain an odd number. There are also odd numbers in the even bisection, precisely all the terms of A246156 in some order, together with all even numbers larger than 2 that are also there. See also comments in A246201.
%H A246202 Antti Karttunen, <a href="/A246202/b246202.txt">Table of n, a(n) for n = 1..638</a>
%H A246202 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a>
%H A246202 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a>
%F A246202 a(1) = 1, a(2n) = A091242(a(n)), a(2n+1) = A014580(a(n)).
%F A246202 As a composition of related permutations:
%F A246202 a(n) = A245702(A054429(n)).
%F A246202 a(n) = A246162(A003188(n)).
%F A246202 a(n) = A193231(A246204(n)).
%F A246202 a(n) = A246164(A193231(n)).
%F A246202 a(n) = A260426(A260422(n)).
%F A246202 Other identities:
%F A246202 For all n > 1, A091225(a(n)) = A000035(n). [After 1, maps even numbers to binary representations of reducible GF(2) polynomials and odd numbers to the corresponding representations of irreducible polynomials, in some order. A246204 has the same property].
%o A246202 (PARI)
%o A246202 allocatemem((2^31)+(2^30));
%o A246202 uplim = (2^25) + (2^24);
%o A246202 v014580 = vector(2^24);
%o A246202 v091242 = vector(uplim);
%o A246202 isA014580(n)=polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from _Charles R Greathouse IV_
%o A246202 i=0; j=0; n=2; while((n < uplim), if(isA014580(n), i++; v014580[i] = n, j++; v091242[j] = n); n++)
%o A246202 A246202(n) = if(1==n, 1, if(0==(n%2), v091242[A246202(n/2)], v014580[A246202((n-1)/2)]));
%o A246202 for(n=1, 638, write("b246202.txt", n, " ", A246202(n)));
%o A246202 \\ Works with PARI Version 2.7.4. - _Antti Karttunen_, Jul 25 2015
%o A246202 (Scheme, with memoization-macro definec)
%o A246202 (definec (A246202 n) (cond ((< n 2) n) ((odd? n) (A014580 (A246202 (/ (- n 1) 2)))) (else (A091242 (A246202 (/ n 2))))))
%Y A246202 Inverse: A246201.
%Y A246202 Similar or related permutations: A245702, A246162, A246164, A246204, A237126, A003188, A054429, A193231, A260422, A260426.
%Y A246202 Cf. A014580, A091242, A091225, A246156.
%K A246202 nonn,tabf
%O A246202 1,2
%A A246202 _Antti Karttunen_, Aug 19 2014