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A309342 a(1) = 0, and for n >= 1, a(n+1) is the number of times the binary representation of a(n) appears in the concatenation of the binary representations of a(1), ..., a(n-1).

%I A309342 #10 Jul 24 2019 22:44:43
%S A309342 0,0,1,0,2,1,2,2,3,1,7,1,11,2,5,5,7,7,9,0,12,1,30,2,12,2,14,4,3,26,4,
%T A309342 4,5,15,13,7,24,0,34,0,39,2,27,3,45,3,49,0,49,1,89,2,36,2,39,3,60,3,
%U A309342 66,1,112,2,45,4,19,6,26,6,28,6,30,12,12,13,20,4
%N A309342 a(1) = 0, and for n >= 1, a(n+1) is the number of times the binary representation of a(n) appears in the concatenation of the binary representations of a(1), ..., a(n-1).
%C A309342 This sequence is a binary variant of A276457.
%C A309342 This sequence is necessarily unbounded.
%H A309342 Rémy Sigrist, <a href="/A309342/b309342.txt">Table of n, a(n) for n = 1..10000</a>
%H A309342 Rémy Sigrist, <a href="/A309342/a309342.png">Logarithmic scatterplot of the first 250000 terms</a>
%H A309342 Rémy Sigrist, <a href="/A309342/a309342.pl.txt">Perl program for A309342</a>
%e A309342 The first terms, alongside the binary representations of a(n) and of a(1), ..., a(n-1) with marks in front of occurrences of a(n), are:
%e A309342   n   a(n)  bin(a(n))  bin(a(1)...a(n-1))
%e A309342   --  ----  ---------  --------------------
%e A309342    1     0          0
%e A309342    2     0          0                    [0
%e A309342    3     1          1                    00
%e A309342    4     0          0                 [0[01
%e A309342    5     2         10                 00[10
%e A309342    6     1          1              00[10[10
%e A309342    7     2         10             00[10[101
%e A309342    8     2         10          00[10[101[10
%e A309342    9     3         11          001010[11010
%e A309342   10     1          1  00[10[10[1[10[10[1[1
%e A309342   11     7        111       00101011010[111
%o A309342 (Perl) See Links section.
%Y A309342 Cf. A276457.
%K A309342 nonn,base
%O A309342 1,5
%A A309342 _Rémy Sigrist_, Jul 24 2019