A173070 Palindromic mountain numbers.

1, 121, 131, 141, 151, 161, 171, 181, 191, 12321, 12421, 12521, 12621, 12721, 12821, 12921, 13431, 13531, 13631, 13731, 13831, 13931, 14541, 14641, 14741, 14841, 14941, 15651, 15751, 15851, 15951, 16761, 16861, 16961, 17871, 17971, 18981

Offset

1,2

Comments

There are 256 terms, the last of which is 12345678987654321. - Michael S. Branicky, Aug 04 2022

Links

Michael S. Branicky, Table of n, a(n) for n = 1..256 (full sequence)

Example

13731 is in the sequence because it is a palindrome (A002113) and it is also a mountain number (A134941).
. . . . .
. . . . .
. . 7 . .
. . . . .
. . . . .
. . . . .
. 3 . 3 .
. . . . .
1 . . . 1

Prog

(Python)
from itertools import chain, combinations as combs
def c(s): return s[0] == s[-1] == 1 and s == s[::-1]
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 = [1] + sorted(int("".join(map(str, t))) for t in s if c(t))
print(afull[:40]) # Michael S. Branicky, Aug 04 2022

Crossrefs

Cf. A002113, A134941, A134951, A134810, A134853, A173071

Sequence in context: A134328 A113614 A134941 * A044867 A162531 A050697

Adjacent sequences: A173067 A173068 A173069 * A173071 A173072 A173073

Keyword

nonn,base,fini,full

Author

Omar E. Pol, Feb 09 2010

Status

approved