

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
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OFFSET

1,2


LINKS

Table of n, a(n) for n=1..51.


FORMULA

Conjectures from Colin Barker, Apr 09 2020: (Start)
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)


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))
Sequence in context: A026266 A334389 A075163 * A143693 A143694 A037476
Adjacent sequences: A333902 A333903 A333904 * A333906 A333907 A333908


KEYWORD

base,nonn


AUTHOR

Eric Angelini, Apr 09 2020


STATUS

approved



