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

1,3

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

Prog

(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

Crossrefs

Cf. A110784.

Sequence in context: A030147 A207954 A193412 * A154562 A193409 A280823

Adjacent sequences: A266136 A266137 A266138 * A266140 A266141 A266142

Keyword

nonn,easy,base

Author

Chai Wah Wu, Dec 25 2015

Status

approved