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 A079313 #24 Dec 17 2024 22:53:52
%S A079313 1,3,5,2,7,8,9,11,13,12,15,17,19,16,21,23,25,20,27,29,31,24,33,35,37,
%T A079313 28,39,41,43,32,45,47,49,36,51,53,55,40,57,59,61,44,63,65,67,48,69,71,
%U A079313 73,52,75,77,79,56,81,83,85,60,87,89,91,64,93,95,97,68,99,101,103,72,105
%N A079313 a(n) is taken to be the smallest positive integer not already present which is consistent with the condition "n is a member of the sequence if and only if a(n) is odd".
%C A079313 The sequence obeys the rule: "The concatenation of a(n) and a(a(n)) is odd". Example: "1" and the 1st term, concatenated, is 11; "3" and the 3rd term, concatenated, is 35; "5" and the 5th term, concatenated, is 57; "2" and the 2nd term, concatenated, is 23; etc.
%H A079313 Michael De Vlieger, <a href="/A079313/b079313.txt">Table of n, a(n) for n = 1..10000</a>
%H A079313 Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.cs.uwaterloo.ca/journals/JIS/VOL6/Cloitre/cloitre2.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2.
%H A079313 Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="https://arxiv.org/abs/math/0305308">Numerical analogues of Aronson's sequence</a>, arXiv:math/0305308 [math.NT], 2003.
%H A079313 <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,2,0,0,0,-1).
%F A079313 For n >= 5 a(n) is given by: a(4t-2) = 4t, a(4t-1) = 6t-3, a(4t) = 6t-1, a(4t+1) = 6t+1.
%F A079313 All odd numbers occur; the only even numbers which occur are 2 and the multiples of 4 excluding 4 itself.
%F A079313 From _Chai Wah Wu_, Apr 13 2024: (Start)
%F A079313 a(n) = 2*a(n-4) - a(n-8) for n > 12.
%F A079313 G.f.: x*(-3*x^11 + 2*x^10 - x^9 + 7*x^7 - x^6 + 2*x^5 + 5*x^4 + 2*x^3 + 5*x^2 + 3*x + 1)/(x^8 - 2*x^4 + 1). (End)
%t A079313 Rest@ CoefficientList[Series[x*(-3*x^11 + 2*x^10 - x^9 + 7*x^7 - x^6 + 2*x^5 + 5*x^4 + 2*x^3 + 5*x^2 + 3*x + 1)/(x^8 - 2*x^4 + 1), {x, 0, 120}], x] (* _Michael De Vlieger_, Dec 17 2024 *)
%Y A079313 Equals A080032 + 1. Cf. A079000, A079250-A079259, A080029-A080031.
%K A079313 easy,nonn
%O A079313 1,2
%A A079313 J. C. Lagarias and _N. J. A. Sloane_, Feb 11 2003
%E A079313 More terms from _Matthew Vandermast_, Mar 20 2003