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%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
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