OFFSET
1,1
COMMENTS
This is the lexicographically earliest sequence having this property, with a(1) = 10. The terms after a(39) = 135708246 are hard to compute. No obvious pattern is visible, though there must be one for sure. "Increasing order" is not "monotonically increasing order".
EXAMPLE
a(1) = 10 because, starting on 0, you'll need n = 1 step to visit all digits (single 0 --> single 1);
a(2) = 100 because, starting on any 0, you'll need at least n = 2 steps to visit all the digits (rightmost 0 --> leftmost 0 --> single 1);
a(3) = 101 because, starting on 0, you'll need at least n = 3 steps to visit all the digits (single 0 --> any 1 --> single 0 --> other 1);
a(4) = 1011 because, starting on 0, you'll need at least n = 4 steps to visit all the digits (single 0 --> leftmost 1 --> single 0 --> middle 1 --> rightmost 1);
a(5) = 1001 because, starting on any 0, you'll need at least n = 5 steps to visit all the digits (leftmost 0 --> rightmost 0 --> rightmost 1 --> rightmost 0 --> leftmost 0 --> leftmost 1);
a(6) = 1320 because, starting on 0, you'll need at least n = 6 steps to visit all the digits (your path will be 0-2-3-1-3-2-3 = 6 steps); etc.
CROSSREFS
KEYWORD
base,nonn
AUTHOR
Eric Angelini and Jean-Marc Falcoz, Jul 27 2020
STATUS
approved