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

Author

Omar E. Pol, Feb 09 2010

Keywords

• nonn
• base
• fini
• full

Comments

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

Examples

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

Links

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

Crossrefs

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

Programs

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