

A333905


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


0



1, 2, 3, 4, 5, 6, 10, 8, 20, 16, 40, 32, 80, 64, 160, 128, 320, 256, 640, 512, 1280, 1024, 2560, 2048, 5120, 4096, 10240, 8192, 20480, 16384, 40960, 32768, 81920, 65536, 163840, 131072, 327680, 262144, 655360, 524288, 1310720, 1048576, 2621440, 2097152, 5242880, 4194304, 10485760, 8388608, 20971520, 16777216, 41943040
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


LINKS



FORMULA

G.f.: x*(1 + 2*x + x^2  x^4  2*x^5  4*x^7) / (1  2*x^2).
a(n) = 2*a(n2) for n>6.
(End)
Conjecture: a(n) = 2^((n7)/2)*(5 + 2*sqrt(2) + (2*sqrt(2)  5)*(1)^n) for n > 6.  Stefano Spezia, Oct 23 2021


EXAMPLE

a(1) = 1 divides 23 (and 23 is a(2) = 2 concatenated to a(3) = 3);
a(2) = 2 divides 34 (and 34 is a(3) = 3 concatenated to a(4) = 4);
a(3) = 3 divides 45 (and 45 is a(4) = 4 concatenated to a(5) = 5);
a(4) = 4 divides 56 (and 56 is a(5) = 5 concatenated to a(6) = 6);
a(5) = 5 divides 610 (and 610 is a(6) = 6 concatenated to a(7) = 10);
a(6) = 6 divides 108 (and 108 is a(7) = 10 concatenated to a(8) = 8);
From a(7) = 10 on, the pattern of the sequence is regular.


CROSSREFS

Cf. A085946 (a(1) = 1, a(2) = 2 and a(n) = smallest number not included earlier that divides the concatenation a(n2), a(n1)).


KEYWORD

base,nonn


AUTHOR



STATUS

approved



