OFFSET
1,2
COMMENTS
This sequence is conjectured to be a permutation of the positive integers.
LINKS
Jean-Marc 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
KEYWORD
base,nonn
AUTHOR
Jean-Marc Falcoz and Eric Angelini, Dec 09 2018
STATUS
approved