

A322467


Lexicographically first sequence of distinct terms such that a(n) is duplicated a(n) digits to the right.


2



1, 10, 2, 3, 20, 30, 5, 6, 4, 105, 46, 7, 11, 8, 12, 9, 70, 208, 21, 190, 120, 130, 13, 14, 15, 17, 18, 22, 16, 131, 140, 154, 61, 71, 181, 60, 32, 23, 24, 27, 28, 29, 31, 35, 25, 36, 40, 170, 42, 302, 41, 43, 270, 280, 292, 531, 110, 53, 54, 613, 62, 160, 400, 47, 104, 200, 410, 34, 300, 19, 38, 1200, 44, 33, 37, 45
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OFFSET

1,2


COMMENTS

This sequence is conjectured to be a permutation of the positive integers.


LINKS

JeanMarc Falcoz, Table of n, a(n) for n = 1..1501


EXAMPLE

The sequence starts with 1,10,2,3,20,30,5,6,4,105,...
a(1) = 1 forces the next digit to be 1;
a(2) = 10 as 10 is the smallest available integer starting with 1 and not leading to a contradiction; this 10 will be duplicated 10 digits to the right;
a(3) = 2 as 2 is the smallest available integer not leading to a contradiction; this 2 will be duplicated 2 digits to the right;
a(4) = 3 as 3 is the smallest available integer not leading to a contradiction; this 3 will be duplicated 3 digits to the right;
a(5)= 20 as 20 is the smallest available integer starting with 2 and not leading to a contradiction; this 20 will be duplicated 20 digits to the right;
a(6) = 30 as 30 is the smallest available integer starting with 3 and not leading to a contradiction; this 30 will be duplicated 30 digits to the right;
Could a(7) be equal to 4? No, because this 4 cannot be duplicated 4 digits to the right as there is already a 0 there (this 0 comes from the duplicated 10);
Thus a(7) = 5 as 5 is the smallest available integer not leading to a contradiction; this 5 will be duplicated 5 digits to the right;
Could a(8) be equal to 4? No, because this 4 cannot be duplicated 4 digits to the right as there is already a 5 there (this 5 comes from the duplicated 5);
Thus a(8) = 6 as 6 is the smallest available integer not leading to a contradiction; this 6 will be duplicated 6 digits to the right;
a(9) = 4 as 4 is the smallest available integer not leading to a contradiction; this 4 will be duplicated 4 digits to the right;
a(10) = 105 as 105 is the smallest available integer starting with 10, followed by 5, and not leading to a contradiction; this 105 will be duplicated 105 digits to the right.
Etc.


CROSSREFS

Sequence in context: A160136 A333478 A336954 * A342078 A049296 A220468
Adjacent sequences: A322464 A322465 A322466 * A322468 A322469 A322470


KEYWORD

base,nonn


AUTHOR

JeanMarc Falcoz and Eric Angelini, Dec 09 2018


STATUS

approved



