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A183086 Generalized canyon numbers.

%I A183086 #14 Aug 03 2022 02:34:32
%S A183086 101,102,103,104,105,106,107,108,109,201,202,203,204,205,206,207,208,
%T A183086 209,212,213,214,215,216,217,218,219,301,302,303,304,305,306,307,308,
%U A183086 309,312,313,314,315,316,317,318,319,323,324,325,326,327,328,329,401,402,403,404,405,406,407,408,409,412
%N A183086 Generalized canyon numbers.
%C A183086 Supersequence of A134970. The structure of digits represents a canyon (a deep valley between cliffs). The first digits are in decreasing order. The last digits are in increasing order. There is only one smaller digit which represents the bottom of the canyon. But the restriction that both cliffs are at same level (first digit equal to the final digit) is dropped here.
%C A183086 This sequence is finite. The final term is 9876543210123456789.
%C A183086 Question: How many terms are there in this sequence?
%C A183086 There are 347489 terms in the sequence. They may be generated in seconds using the posted Python program. - _Michael S. Branicky_, Aug 02 2022
%H A183086 Michael S. Branicky, <a href="/A183086/b183086.txt">Table of n, a(n) for n = 1..10000</a>
%e A183086 Illustration of 751378 as a generalized canyon number:
%e A183086   . . . . . .
%e A183086   . . . . . 8
%e A183086   7 . . . 7 .
%e A183086   . . . . . .
%e A183086   . 5 . . . .
%e A183086   . . . . . .
%e A183086   . . . 3 . .
%e A183086   . . . . . .
%e A183086   . . 1 . . .
%e A183086   . . . . . .
%o A183086 (Python)
%o A183086 from itertools import chain, combinations as combs
%o A183086 ups = list(chain.from_iterable(combs(range(10), r) for r in range(2, 11)))
%o A183086 s = set(L[::-1] + R[1:] for L in ups for R in ups if L[0] == R[0])
%o A183086 afull = sorted(int("".join(map(str, t))) for t in s)
%o A183086 print(afull[:60]) # _Michael S. Branicky_, Aug 02 2022
%Y A183086 Cf. A134853, A134970, A183087.
%K A183086 nonn,base,fini
%O A183086 1,1
%A A183086 _Omar E. Pol_, Jan 19 2011