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A336611
Always start on the lowest digit of a(n), then visit all digits of a(n) in increasing order. The terms of the sequence are the smallest one that force the visitor to walk n steps to complete his tour (a single step drives you from a digit to the closest one).
2
10, 100, 101, 1011, 1001, 1320, 1302, 10210, 10201, 13002, 13042, 102013, 102031, 130024, 130042, 135204, 135024, 1024013, 1035024, 1305204, 1305024, 1350024, 1350624, 10240513, 10350624, 13050024, 13050624, 13500264, 13500624, 13572046, 13570246, 103572046, 103570246, 130572046, 130570246, 135072046
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
Cf. A284591.
Sequence in context: A115794 A105424 A115832 * A342215 A342135 A169665
KEYWORD
base,nonn
AUTHOR
STATUS
approved