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A134853 Generalized mountain numbers.

%I A134853 #20 Aug 03 2022 02:37:35
%S A134853 1,2,3,4,5,6,7,8,9,120,121,130,131,132,140,141,142,143,150,151,152,
%T A134853 153,154,160,161,162,163,164,165,170,171,172,173,174,175,176,180,181,
%U A134853 182,183,184,185,186,187,190,191,192,193,194,195,196
%N A134853 Generalized mountain numbers.
%C A134853 a(1) to a(9) are equal to A000027. For n>9 the structure of the digits represents a mountain. The first digits are in increasing order. The last digits are in decreasing order. There is only one largest digit which represents the top of the mountain. This sequence is finite. The last member is 123456789876543210.
%C A134853 The sequence is a supersequence of A134941, because the restriction that both feet of the mountain are at "sea level" (first and last digit equal 1) is dropped here.
%C A134853 There are 173247 terms in this sequence. - _Nathaniel Johnston_, Dec 29 2010
%H A134853 Michael S. Branicky, <a href="/A134853/b134853.txt">Table of n, a(n) for n = 1..10000</a>
%e A134853 The number of this sequence (A134853) is a generalized mountain number.
%e A134853 . . . . . .
%e A134853 . . . 8 . .
%e A134853 . . . . . .
%e A134853 . . . . . .
%e A134853 . . . . 5 .
%e A134853 . . 4 . . .
%e A134853 . 3 . . . 3
%e A134853 . . . . . .
%e A134853 1 . . . . .
%e A134853 . . . . . .
%o A134853 (Python)
%o A134853 from itertools import chain, combinations as combs
%o A134853 ups = list(chain.from_iterable(combs(range(10), r) for r in range(2, 11)))
%o A134853 s = set(L[:-1] + R[::-1] for L in ups for R in ups if L[-1] == R[-1])
%o A134853 afull = list(range(1, 10))
%o A134853 afull += sorted(int("".join(map(str, t))) for t in s if t[0] != 0)
%o A134853 print(afull[:60]) # _Michael S. Branicky_, Aug 02 2022
%Y A134853 Cf. A134941, A134951, A178912.
%K A134853 base,fini,nonn
%O A134853 1,2
%A A134853 _Omar E. Pol_, Nov 26 2007, corrected May 15 2008
%E A134853 Better definition and edited by _Omar E. Pol_, Nov 11 2009