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 A246163 #17 Aug 20 2014 23:58:45 %S A246163 1,2,7,3,6,9,8,5,10,27,4,24,11,15,30,45,12,40,26,29,17,34,119,20,25, %T A246163 120,46,39,51,102,14,153,60,43,136,114,31,105,85,170,44,18,427,68,125, %U A246163 408,13,150,33,187,255,510,116,54,41,765,204,135,28,680,16,23,442,99,461,257,35,514,156,90,123,1799,118,340,393,36 %N A246163 Permutation of natural numbers: a(1) = 1, a(A014580(n)) = A065621(1+a(n)), a(A091242(n)) = A048724(a(n)), where A065621(n) and A048724(n) give the reversing binary representation of n and -n, respectively, and A014580 resp. A091242 are the binary coded irreducible resp. reducible polynomials over GF(2). %C A246163 This is an instance of entanglement permutation, where the two complementary pairs to be entangled with each other are A014580/A091242 (binary codes for irreducible and reducible polynomials over GF(2)) and A065621/A048724, the latter which themselves are permutations of A000069/A001969 (odious and evil numbers), which means that this permutation shares many properties with A246161. %C A246163 Because 3 is the only evil number in A014580, it implies that, apart from a(3)=7, odious numbers occur in odious positions only (along with many evil numbers that also occur in odious positions). %C A246163 Furthermore, all terms of A246158 reside in infinite cycles, and apart from 4 and 8, all of them reside in separate cycles. The infinite cycle containing 4 and 8 goes as: ..., 2091, 97, 47, 13, 11, 4, 3, 7, 8, 5, 6, 9, 10, 27, 46, 408, 2535, ... and it is only because a(3) = 7, that it can temporarily switch back from evil terms to odious terms, until right after a(8) = 5 it is finally doomed to the eternal evilness. %C A246163 Please see also the comments at A246201 and A246161. %H A246163 Antti Karttunen, <a href="/A246163/b246163.txt">Table of n, a(n) for n = 1..10001</a> %H A246163 <a href="/index/Ge#GF2X">Index entries for sequences operating on GF(2)[X]-polynomials</a> %H A246163 <a href="/index/Per#IntegerPermutation">Index entries for sequences that are permutations of the natural numbers</a> %F A246163 a(1) = 1, and for n > 1, if n is in A014580, a(n) = A065621(1+a(A091226(n))), otherwise a(n) = A048724(a(A091245(n))). %F A246163 As a composition of related permutations: %F A246163 a(n) = A193231(A246201(n)). %F A246163 a(n) = A234026(A245701(n)). %F A246163 a(n) = A234612(A246161(n)). %F A246163 a(n) = A193231(A246203(A193231(n))). %F A246163 Other identities: %F A246163 For all n > 1, A010060(a(n)) = A091225(n). [Maps binary representations of irreducible GF(2) polynomials (A014580) to odious numbers and the corresponding representations of reducible polynomials (A091242) to evil numbers, in some order]. %o A246163 (Scheme, with memoization-macro definec) %o A246163 (definec (A246163 n) (cond ((= 1 n) n) ((= 1 (A091225 n)) (A065621 (+ 1 (A246163 (A091226 n))))) (else (A048724 (A246163 (A091245 n)))))) %Y A246163 Inverse: A246164. %Y A246163 Similar or related permutations: A246205, A193231, A246201, A234026, A245701, A234612, A246161, A246203. %Y A246163 Cf. A010060, A014580, A048724, A065621, A091225, A091226, A091245. %K A246163 nonn %O A246163 1,2 %A A246163 _Antti Karttunen_, Aug 19 2014