A266139 Volcano palindromes: palindromes not in A110784 such that removing one digit will result in a term in A110784.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 101, 202, 212, 303, 313, 323, 404, 414, 424, 434, 505, 515, 525, 535, 545, 606, 616, 626, 636, 646, 656, 707, 717, 727, 737, 747, 757, 767, 808, 818, 828, 838, 848, 858, 868, 878, 909, 919, 929, 939, 949, 959, 969, 979, 989, 11011

Offset: 1

Author

Chai Wah Wu, Dec 25 2015

Keywords

• nonn
• easy
• base

Comments

All terms have odd number of digits. Terms are palindromes such that digits are nondecreasing halfway through except for the middle digit, which is strictly smaller than its neighboring digits.

Illustration using a term of this sequence, 23446564432:

. . . . 6 . 6 . . . .

. . . . . 5 . . . . .

. . 4 4 . . . 4 4 . .

. 3 . . . . . . . 3 .

2 . . . . . . . . . 2

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A110784.

Programs

Python

from itertools import combinations_with_replacement as mc
def agentod(digits):
    yield from range(10)
    for d in range(3, digits+1, 2):
        for left in mc("123456789", d//2):
            for center in range(int(left[-1])):
                yield int("".join(left + (str(center), ) + left[::-1]))
print([an for an in agentod(5)]) # Michael S. Branicky, Aug 21 2021