A322467 Lexicographically first sequence of distinct terms such that a(n) is duplicated a(n) digits to the right.

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

Offset: 1

Author

Jean-Marc Falcoz and Eric Angelini, Dec 09 2018

Keywords

• base
• nonn

Comments

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

Examples

			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.
		

Links

• Jean-Marc Falcoz, Table of n, a(n) for n = 1..1501