A134941 Mountain numbers.

1, 121, 131, 141, 151, 161, 171, 181, 191, 1231, 1241, 1251, 1261, 1271, 1281, 1291, 1321, 1341, 1351, 1361, 1371, 1381, 1391, 1421, 1431, 1451, 1461, 1471, 1481, 1491, 1521, 1531, 1541, 1561, 1571, 1581, 1591, 1621, 1631, 1641, 1651, 1671, 1681, 1691, 1721

Offset

1,2

Comments

For n > 1 the structure of digits represents a mountain. The first digit is 1. The last digit is 1. The first digits are in increasing order. The last digits are in decreasing order. The numbers only have one largest digit. This sequence is finite. The last term is 12345678987654321.

The total number of terms is 21846. - Hans Havermann, Nov 25 2007

A002450(8) + 1 = 21846. - Reinhard Zumkeller, May 17 2010

From Reinhard Zumkeller, May 25 2010: (Start)

A178333 is the characteristic function of mountain numbers: A178333(a(n)) = 1;

A178334(n) is the number of mountain numbers <= n;

A178052 and A178053 give sums of digits and digital roots of mountain numbers;

A178051(n) is the peak value of the n-th mountain number. (End)

Links

Joshua Zucker, Table of n, a(n) for n = 1..21846 (shows all terms).

Example

The A-number of this sequence (A134941) is itself a mountain number:
  . . . 9 . .
  . . . . . .
  . . . . . .
  . . . . . .
  . . . . . .
  . . 4 . 4 .
  . 3 . . . .
  . . . . . .
  1 . . . . 1

Mathematica

mountainQ[n_] := MatchQ[ IntegerDigits[n], {1, a___, b_, c___, 1} /; OrderedQ[{1, a, b}, Less] && OrderedQ[ Reverse[{b, c, 1}], Less]]; mountainQ[1] = True; Select[Range[2000], mountainQ] (* Jean-François Alcover, Jun 13 2012 *)
Prepend[Union @@ ((FromDigits@#&/@Flatten[Table[Join[(k=Prepend[#, 1]&/@
Subsets[Range[2, #-1]])[[i]], {#}, (Reverse@# & /@k)[[j]]],
{i, 2^(# - 2)}, {j, 2^(# - 2)}], 1])&/@Range[9]), 1] (* Hans Rudolf Widmer, Apr 30 2024 *)

Prog

(Haskell)
import Data.List (elemIndices)
a134941 n = a134941_list !! (n-1)
a134941_list = elemIndices 1 a178333_list
-- Reinhard Zumkeller, Oct 28 2001
(Python)
from itertools import product
def ups():
    d = "23456789"
    for b in product([0, 1], repeat=8):
        yield "1" + "".join(d[i]*b[i] for i in range(8))
def downsfrom(apex):
    if apex < 3: yield "1"*int(apex==2); return
    d = "8765432"[-(apex-2):]
    for b in product([0, 1], repeat=len(d)):
        yield "".join(d[i]*b[i] for i in range(len(d))) + "1"
def A134941(): # return full sequence as a list
    mountain_strs = (u+d for u in ups() for d in downsfrom(int(u[-1])))
    return sorted(int(ms) for ms in mountain_strs)
print(A134941()[:45]) # Michael S. Branicky, Dec 31 2021

Crossrefs

Cf. A134853, A135417, A134951, A182721.

Cf. A115300, A175044. - Reinhard Zumkeller, May 25 2010

Sequence in context: A055468 A134328 A113614 * A173070 A044867 A162531

Adjacent sequences: A134938 A134939 A134940 * A134942 A134943 A134944

Keyword

base,fini,full,nonn

Author

Omar E. Pol, Nov 22 2007

Status

approved