

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
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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

Table of n, a(n) for n=1..36.


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 0231323 = 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 JeanMarc Falcoz, Jul 27 2020


STATUS

approved



