

A134853


Generalized mountain numbers.


10



1, 2, 3, 4, 5, 6, 7, 8, 9, 120, 121, 130, 131, 132, 140, 141, 142, 143, 150, 151, 152, 153, 154, 160, 161, 162, 163, 164, 165, 170, 171, 172, 173, 174, 175, 176, 180, 181, 182, 183, 184, 185, 186, 187, 190, 191, 192, 193, 194, 195, 196
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OFFSET

1,2


COMMENTS

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.
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.
There are 173247 terms in this sequence.  Nathaniel Johnston, Dec 29 2010


LINKS

Michael S. Branicky, Table of n, a(n) for n = 1..10000


EXAMPLE

The number of this sequence (A134853) is a generalized mountain number.
. . . . . .
. . . 8 . .
. . . . . .
. . . . . .
. . . . 5 .
. . 4 . . .
. 3 . . . 3
. . . . . .
1 . . . . .
. . . . . .


PROG

(Python)
from itertools import chain, combinations as combs
ups = list(chain.from_iterable(combs(range(10), r) for r in range(2, 11)))
s = set(L[:1] + R[::1] for L in ups for R in ups if L[1] == R[1])
afull = list(range(1, 10))
afull += sorted(int("".join(map(str, t))) for t in s if t[0] != 0)
print(afull[:60]) # Michael S. Branicky, Aug 02 2022


CROSSREFS

Cf. A134941, A134951, A178912.
Sequence in context: A082232 A117228 A032567 * A193407 A134810 A173689
Adjacent sequences: A134850 A134851 A134852 * A134854 A134855 A134856


KEYWORD

base,fini,nonn


AUTHOR

Omar E. Pol, Nov 26 2007, corrected May 15 2008


EXTENSIONS

Better definition and edited by Omar E. Pol, Nov 11 2009


STATUS

approved



