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A308830 a(n) is the smallest positive integer such that the concatenation, in base 2, of the first n terms is divisible by n.

%I A308830 #11 Jun 29 2019 01:59:12
%S A308830 1,2,3,4,5,2,9,8,5,2,3,20,7,14,27,16,11,30,11,20,15,22,31,24,11,14,11,
%T A308830 20,15,10,35,32,1,26,97,92,53,18,31,56,91,10,3,12,27,30,15,48,37,78,
%U A308830 23,108,9,6,49,8,51,54,87,60,79,26,25,64,111,122,117,28
%N A308830 a(n) is the smallest positive integer such that the concatenation, in base 2, of the first n terms is divisible by n.
%C A308830 This sequence is the binary variant of A099552.
%H A308830 Rémy Sigrist, <a href="/A308830/b308830.txt">Table of n, a(n) for n = 1..8192</a>
%H A308830 Rémy Sigrist, <a href="/A308830/a308830.gp.txt">PARI program for A308830</a>
%F A308830 a(2^k) = 2^k for any k >= 0.
%F A308830 A007814(a(n)) = A007814(n).
%e A308830 The first terms, alongside the concatenation of the first n terms, both in decimal and in base 2, are:
%e A308830   n   a(n)  bin(a(n))  K(n)      bin(K(n))
%e A308830   --  ----  ---------  --------  --------------------------
%e A308830    1     1          1         1                           1
%e A308830    2     2         10         6                         110
%e A308830    3     3         11        27                       11011
%e A308830    4     4        100       220                    11011100
%e A308830    5     5        101      1765                 11011100101
%e A308830    6     2         10      7062               1101110010110
%e A308830    7     9       1001    113001           11011100101101001
%e A308830    8     8       1000   1808024       110111001011010011000
%e A308830    9     5        101  14464197    110111001011010011000101
%e A308830   10     2         10  57856790  11011100101101001100010110
%o A308830 (PARI) See Links section.
%Y A308830 Cf. A007814, A099552.
%K A308830 nonn,base
%O A308830 1,2
%A A308830 _Rémy Sigrist_, Jun 27 2019