A134853 - OEIS

%I #20 Aug 03 2022 02:37:35

%S 1,2,3,4,5,6,7,8,9,120,121,130,131,132,140,141,142,143,150,151,152,

%T 153,154,160,161,162,163,164,165,170,171,172,173,174,175,176,180,181,

%U 182,183,184,185,186,187,190,191,192,193,194,195,196

%N Generalized mountain numbers.

%C 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 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 There are 173247 terms in this sequence. - _Nathaniel Johnston_, Dec 29 2010

%H Michael S. Branicky, <a href="/A134853/b134853.txt">Table of n, a(n) for n = 1..10000</a>

%e The number of this sequence (A134853) is a generalized mountain number.

%e . . . . . .

%e . . . 8 . .

%e . . . . . .

%e . . . . . .

%e . . . . 5 .

%e . . 4 . . .

%e . 3 . . . 3

%e . . . . . .

%e 1 . . . . .

%e . . . . . .

%o (Python)

%o from itertools import chain, combinations as combs

%o ups = list(chain.from_iterable(combs(range(10), r) for r in range(2, 11)))

%o s = set(L[:-1] + R[::-1] for L in ups for R in ups if L[-1] == R[-1])

%o afull = list(range(1, 10))

%o afull += sorted(int("".join(map(str, t))) for t in s if t[0] != 0)

%o print(afull[:60]) # _Michael S. Branicky_, Aug 02 2022

%Y Cf. A134941, A134951, A178912.

%K base,fini,nonn

%O 1,2

%A _Omar E. Pol_, Nov 26 2007, corrected May 15 2008

%E Better definition and edited by _Omar E. Pol_, Nov 11 2009