cp's OEIS Frontend

A336515 a(1) = 1, and for any n > 0, a(n+1) is the number of k in the range 1..n such that the binary representation of a(k) appears as a substring in the binary representation of a(n).

%I A336515 #12 Jul 25 2020 11:08:52
%S A336515 1,1,2,3,3,4,4,5,4,6,6,7,5,5,6,8,7,6,9,7,7,8,8,9,8,10,7,9,9,10,8,11,9,
%T A336515 11,10,9,12,13,13,14,15,10,10,11,11,12,14,16,12,15,11,13,15,12,16,13,
%U A336515 16,14,17,12,17,13,17,14,18,13,18,14,19,15,13,19,16
%N A336515 a(1) = 1, and for any n > 0, a(n+1) is the number of k in the range 1..n such that the binary representation of a(k) appears as a substring in the binary representation of a(n).
%C A336515 This sequence is unbounded.
%H A336515 Rémy Sigrist, <a href="/A336515/b336515.txt">Table of n, a(n) for n = 1..10000</a>
%H A336515 Rémy Sigrist, <a href="/A336515/a336515.png">Density plot of the first 100000000 terms</a>
%H A336515 Rémy Sigrist, <a href="/A336515/a336515.gp.txt">PARI program for A336515</a>
%e A336515 The first terms, alongside their binary representation and the corresponding k's, are:
%e A336515   n   a(n)  bin(a(n))  k's
%e A336515   --  ----  ---------  -------------
%e A336515    1     1          1  N/A
%e A336515    2     1          1  {1}
%e A336515    3     2         10  {1, 2}
%e A336515    4     3         11  {1, 2, 3}
%e A336515    5     3         11  {1, 2, 4}
%e A336515    6     4        100  {1, 2, 4, 5}
%e A336515    7     4        100  {1, 2, 3, 6}
%e A336515    8     5        101  {1, 2, 3, 6, 7}
%e A336515    9     4        100  {1, 2, 3, 8}
%e A336515   10     6        110  {1, 2, 3, 6, 7, 9}
%o A336515 (PARI) See Links section.
%Y A336515 Cf. A336514 (decimal variant).
%K A336515 nonn,look,base
%O A336515 1,3
%A A336515 _Rémy Sigrist_, Jul 24 2020