A333905 - OEIS

%I #14 Oct 26 2021 21:33:28

%S 1,2,3,4,5,6,10,8,20,16,40,32,80,64,160,128,320,256,640,512,1280,1024,

%T 2560,2048,5120,4096,10240,8192,20480,16384,40960,32768,81920,65536,

%U 163840,131072,327680,262144,655360,524288,1310720,1048576,2621440,2097152,5242880,4194304,10485760,8388608,20971520,16777216,41943040

%N Lexicographically earliest sequence of distinct positive integers such that a(n) divides the concatenation of a(n+1) to a(n+2).

%F Conjectures from _Colin Barker_, Apr 09 2020: (Start)

%F G.f.: x*(1 + 2*x + x^2 - x^4 - 2*x^5 - 4*x^7) / (1 - 2*x^2).

%F a(n) = 2*a(n-2) for n>6.

%F (End)

%F Conjecture: a(n) = 2^((n-7)/2)*(5 + 2*sqrt(2) + (2*sqrt(2) - 5)*(-1)^n) for n > 6. - _Stefano Spezia_, Oct 23 2021

%e a(1) = 1 divides 23 (and 23 is a(2) = 2 concatenated to a(3) = 3);

%e a(2) = 2 divides 34 (and 34 is a(3) = 3 concatenated to a(4) = 4);

%e a(3) = 3 divides 45 (and 45 is a(4) = 4 concatenated to a(5) = 5);

%e a(4) = 4 divides 56 (and 56 is a(5) = 5 concatenated to a(6) = 6);

%e a(5) = 5 divides 610 (and 610 is a(6) = 6 concatenated to a(7) = 10);

%e a(6) = 6 divides 108 (and 108 is a(7) = 10 concatenated to a(8) = 8);

%e From a(7) = 10 on, the pattern of the sequence is regular.

%Y Cf. A085946 (a(1) = 1, a(2) = 2 and a(n) = smallest number not included earlier that divides the concatenation a(n-2), a(n-1)).

%K base,nonn

%O 1,2

%A _Eric Angelini_, Apr 09 2020