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 A348190 #16 Jan 03 2023 06:15:58 %S A348190 2,2,3,2,3,3,4,2,2,5,3,4,3,5,5,7,5,2,4,2,2,5,4,6,3,2,9,5,9,3,6,10,9,9, %T A348190 6,5,7,4,12,11,11,2,6,4,8,3,4,6,7,13,11,5,5,6,4,8,10,9,13,4,13,4,6,6, %U A348190 2,11,5,4,6,11,18,9,15,2,15,12 %N A348190 Positive integers where each is chosen to be the second smallest number subject to the condition that no three terms a(j), a(j+k), a(j+2*k) (for any j and k) form an arithmetic progression. %C A348190 The sequence seems to behave in a similar way as the "forest fire" A229037. The graph (up to n=5000) looks like it has a fractal structure, with each dense "pillar" approximately double the size of the previous one. %C A348190 The terms of this sequence do not seem to be larger (on average) than those of A229037, despite the construction of this sequence. %H A348190 Neal Gersh Tolunsky, <a href="/A348190/b348190.txt">Table of n, a(n) for n = 1..8000</a> %H A348190 Rémy Sigrist, <a href="/A348190/a348190.gp.txt">PARI program for A348190</a> %H A348190 Neal Gersh Tolunsky, <a href="/A348190/a348190_1.png">Scatterplot for n=1...8000</a> %e A348190 a(7) = 4, because 2 would form an arithmetic progression with a(1) = 2 and a(4) = 2 and 3 would form an arithmetic progression with a(5) = 3 and a(6) = 3. Therefore, 4 is the second smallest number which satisfies the condition (1 being the smallest). %o A348190 (PARI) See Links section. %Y A348190 Cf. A229037. %K A348190 nonn,look %O A348190 1,1 %A A348190 _Albert Böschow_, Oct 06 2021