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A336514 a(1) = 1, and for any n > 0, a(n+1) is the number of k in the range 1..n such that the decimal representation of a(k) appears as a substring in the decimal representation of a(n).

%I A336514 #11 Jul 25 2020 11:44:44
%S A336514 1,1,2,1,3,1,4,1,5,1,6,1,7,1,8,1,9,1,10,11,11,12,12,13,12,14,12,15,12,
%T A336514 16,12,17,12,18,12,19,12,20,2,2,3,2,4,2,5,2,6,2,7,2,8,2,9,2,10,12,30,
%U A336514 3,3,4,3,5,3,6,3,7,3,8,3,9,3,10,13,22,11,13,23
%N A336514 a(1) = 1, and for any n > 0, a(n+1) is the number of k in the range 1..n such that the decimal representation of a(k) appears as a substring in the decimal representation of a(n).
%C A336514 This sequence is unbounded.
%H A336514 Rémy Sigrist, <a href="/A336514/b336514.txt">Table of n, a(n) for n = 1..10000</a>
%H A336514 Rémy Sigrist, <a href="/A336514/a336514.png">Density plot of the first 100000000 terms</a>
%H A336514 Rémy Sigrist, <a href="/A336514/a336514.gp.txt">PARI program for A336514</a>
%e A336514 The first terms, alongside the corresponding k's, are:
%e A336514   n   a(n)  k's
%e A336514   --  ----  -----------
%e A336514    1     1  N/A
%e A336514    2     1  {1}
%e A336514    3     2  {1, 2}
%e A336514    4     1  {3}
%e A336514    5     3  {1, 2, 4}
%e A336514    6     1  {5}
%e A336514    7     4  {1, 2, 4, 6}
%e A336514    8     1  {7}
%e A336514    9     5  {1, 2, 4, 6, 8}
%e A336514   10     1  {9}
%o A336514 (PARI) See Links section.
%Y A336514 Cf. A336515 (binary variant).
%K A336514 nonn,look,base
%O A336514 1,3
%A A336514 _Rémy Sigrist_, Jul 24 2020