A134853 Generalized mountain numbers.

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

Offset: 1

Author

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

Keywords

• base
• fini
• nonn

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

Examples

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

Links

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

Crossrefs

Cf. A134941, A134951, A178912.

Programs

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

Extensions

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