A183086 Generalized canyon numbers.

101, 102, 103, 104, 105, 106, 107, 108, 109, 201, 202, 203, 204, 205, 206, 207, 208, 209, 212, 213, 214, 215, 216, 217, 218, 219, 301, 302, 303, 304, 305, 306, 307, 308, 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

Offset: 1

Author

Omar E. Pol, Jan 19 2011

Keywords

• nonn
• base
• fini

Comments

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.

This sequence is finite. The final term is 9876543210123456789.

Question: How many terms are there in this sequence?

There are 347489 terms in the sequence. They may be generated in seconds using the posted Python program. - Michael S. Branicky, Aug 02 2022

Examples

			Illustration of 751378 as a generalized canyon number:
  . . . . . .
  . . . . . 8
  7 . . . 7 .
  . . . . . .
  . 5 . . . .
  . . . . . .
  . . . 3 . .
  . . . . . .
  . . 1 . . .
  . . . . . .
		

Links

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

Crossrefs

Cf. A134853, A134970, A183087.

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[0] == R[0])
afull = sorted(int("".join(map(str, t))) for t in s)
print(afull[:60]) # Michael S. Branicky, Aug 02 2022