A336515 - OEIS

%I #12 Jul 25 2020 11:08:52

%S 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 11,10,9,12,13,13,14,15,10,10,11,11,12,14,16,12,15,11,13,15,12,16,13,

%U 16,14,17,12,17,13,17,14,18,13,18,14,19,15,13,19,16

%N 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 This sequence is unbounded.

%H Rémy Sigrist, <a href="/A336515/b336515.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A336515/a336515.png">Density plot of the first 100000000 terms</a>

%H Rémy Sigrist, <a href="/A336515/a336515.gp.txt">PARI program for A336515</a>

%e The first terms, alongside their binary representation and the corresponding k's, are:

%e   n   a(n)  bin(a(n))  k's

%e   --  ----  ---------  -------------

%e    1     1          1  N/A

%e    2     1          1  {1}

%e    3     2         10  {1, 2}

%e    4     3         11  {1, 2, 3}

%e    5     3         11  {1, 2, 4}

%e    6     4        100  {1, 2, 4, 5}

%e    7     4        100  {1, 2, 3, 6}

%e    8     5        101  {1, 2, 3, 6, 7}

%e    9     4        100  {1, 2, 3, 8}

%e   10     6        110  {1, 2, 3, 6, 7, 9}

%o (PARI) See Links section.

%Y Cf. A336514 (decimal variant).

%K nonn,look,base

%O 1,3

%A _Rémy Sigrist_, Jul 24 2020