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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). 0
 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 (list; graph; refs; listen; history; text; internal format)
 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". LINKS 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 Adjacent sequences:  A336608 A336609 A336610 * A336612 A336613 A336614 KEYWORD base,nonn AUTHOR Eric Angelini and Jean-Marc Falcoz, Jul 27 2020 STATUS approved

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Last modified July 23 17:41 EDT 2021. Contains 346259 sequences. (Running on oeis4.)