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 A080353 #15 Jul 02 2025 11:34:10 %S A080353 5,7,9,11,12,14,15,17,18,20,21,22,24,25,26,28,29,30,32,33,34,35,37,38, %T A080353 39,40,42,43,44,45,47,48,49,50,51,53,54,55,56,57,59,60,61,62,63,65,66, %U A080353 67,68,69,70,72,73,74,75,76,77,79,80,81,82,83,84,86,87,88,89 %N A080353 a(1)=5; for n>1, a(n)=a(n-1)+1 if n is already in the sequence, a(n)=a(n-1)+2 otherwise. %C A080353 Conjecture: This sequence is equivalent to N \ A008478. - _Michael De Vlieger_, Jul 02 2025 %H A080353 Michael De Vlieger, <a href="/A080353/b080353.txt">Table of n, a(n) for n = 1..10000</a> %H A080353 Benoit Cloitre, <a href="https://arxiv.org/abs/2506.18103">A study of a family of self-referential sequences</a>, arXiv:2506.18103 [math.GM], 2025. See p. 13. %H A080353 Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">Numerical analogues of Aronson's sequence</a>, J. Integer Seqs., Vol. 6 (2003), #03.2.2. %H A080353 Benoit Cloitre, N. J. A. Sloane and M. J. Vandermast, <a href="http://arXiv.org/abs/math.NT/0305308">Numerical analogues of Aronson's sequence</a> (math.NT/0305308) %F A080353 a(n) = n + floor(sqrt(6*n)) + O(1). %t A080353 a[1] = 5; a[n_] := a[n] = If[MemberQ[Array[a, n-1], n], a[n-1]+1, a[n-1]+2]; Array[a, 67] (* _Jean-François Alcover_, Oct 08 2018 *) %Y A080353 Cf. A080036, A080037. Differences give A080354. %K A080353 nonn %O A080353 1,1 %A A080353 _N. J. A. Sloane_, Mar 20 2003