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A134970 Canyon numbers. Numbers with exactly one locally minimal digit and with exactly two locally maximal digits which are the same digit and non-adjacent. 10

%I

%S 101,202,212,303,313,323,404,414,424,434,505,515,525,535,545,606,616,

%T 626,636,646,656,707,717,727,737,747,757,767,808,818,828,838,848,858,

%U 868,878,909,919,929,939,949,959,969,979,989,2012,2102,3013,3023

%N Canyon numbers. Numbers with exactly one locally minimal digit and with exactly two locally maximal digits which are the same digit and non-adjacent.

%C A digit of a number is a local minimum if it is less than (or equal to) its neighboring digit(s). It is a local maximum likewise if it is greater than (or equal to) its neighboring digit(s). For example, 55432123 has three local maxima (the two 5s and the end 3) and one local minimum (the 1).

%C Because they are nonadjacent, the maxima occur at the end (and the minimum somewhere between), and the sequence of digits must be decreasing up to the minimum, then increasing. This may be taken as part of the definition (which entails non-adjacency of the maxima).

%C The structure of digits represent a canyon (a deep valley between cliffs). The first digit is equal to last digit. The first group of digits are in decreasing order. The second group of digits are in increasing order. The digits have a unique smallest digit which represents the bottom of the canyon.

%C This sequence is finite - it has 116505 elements. The largest and final element of the sequence is a(116505) = 9876543210123456789.

%C 9752369 is a canyon number because the unique minimum digit is the 2, and the maximum digit is 9 (at the beginning and end).

%H Kellen Myers, <a href="/A134970/b134970.txt">Table of n, a(n) for n = 1..116505</a>

%e Illustration of 4104 as a canyon number:

%e 4 . . 4

%e . . . .

%e . . . .

%e . 1 . .

%e . . 0 .

%Y Cf. A134971.

%K fini,nonn,base,full

%O 1,1

%A _Omar E. Pol_, Nov 25 2007, Nov 26 2007

%E Edited by _Kellen Myers_, Jan 18 2011

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Last modified January 19 20:41 EST 2020. Contains 331066 sequences. (Running on oeis4.)