A110784 -id:A110784 - cp's OEIS frontend

A266140 Palindromes such that removing at most one digit will result in a term in A110784.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, 131, 141, 151, 161, 171, 181, 191, 202, 212, 222, 232, 242, 252, 262, 272, 282, 292, 303, 313, 323, 333, 343, 353, 363, 373, 383, 393, 404, 414, 424, 434, 444, 454, 464, 474, 484

Offset: 1

Chai Wah Wu, Dec 25 2015

Union of A266139 and A110784. Every palindrome p can have its digits permuted to produce a term m <= p in this sequence, and this sequence is the minimal such sequence (i.e., no term in the sequence can have its digits permuted to form another term in the sequence). Palindromes modulo permutation of digits.
a(n) = A110751(n-1) for 2<=n<=109, which means A110751 contains numbers like 1001 and 1089 which are absent here. - R. J. Mathar, Aug 07 2025
The first entry of A002113 not in this sequence here is 1001. - R. J. Mathar, Aug 07 2025

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

Cf. A110784, A266139.

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

Original entry on oeis.org

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

Chai Wah Wu, Dec 25 2015

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

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

Cf. A110784.

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

A110785 Palindromes in which the digits are in nonincreasing order halfway through.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 202, 212, 222, 303, 313, 323, 333, 404, 414, 424, 434, 444, 505, 515, 525, 535, 545, 555, 606, 616, 626, 636, 646, 656, 666, 707, 717, 727, 737, 747, 757, 767, 777, 808, 818, 828, 838, 848

Offset: 1

Amarnath Murthy, Aug 12 2005

			After 111 the next term is 202 and not 121, 131, up to 191.

Paolo Xausa, Table of n, a(n) for n = 1..10000

Cf. A002113, A110784.

A110785Q[k_] := PalindromeQ[#] && (Length[#] <= 2 || Min[Differences[#[[;;Ceiling[Length[#]/2]]]]] <= 0) & [IntegerDigits[k]];
Select[Range[2000], A110785Q] (* Paolo Xausa, Jul 31 2025 *)

A193408 Hill numbers.

Original entry on oeis.org

1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 111, 121, 131, 141, 151, 161, 171, 181, 191, 222, 232, 242, 252, 262, 272, 282, 292, 333, 343, 353, 363, 373, 383, 393, 444, 454, 464, 474, 484, 494, 555, 565, 575, 585, 595, 666, 676, 686, 696, 777, 787, 797, 888, 898, 999, 1111, 1221, 1231, 1241, 1251, 1261, 1271, 1281, 1291, 1321, 1331

Offset: 1

Jaroslav Krizek, Jul 25 2011

Another version of mountain numbers (A134941) and A193407.
For n > 20 the structure of digits represents a hill. The first digit is equal to the last digit (1 - 9). The first digits are in nondecreasing order. The last digits are in nonincreasing order. The numbers may have more than one largest digit. Sequence is infinite.
Superset of mountain numbers (A134941), A193407, and Giza numbers (A134810).
Superset of A110784. - R. J. Mathar, Aug 07 2011

			Illustration using a term of this sequence, 4566664:
  .  .  6  6  6  6  .
  .  5  .  .  .  .  .
  4  .  .  .  .  .  4

Cf. A110784, A134810, A134941, A193407.

nonz[v_] := Select[v,#!=0 &]; hillQ[n_] := Module[{d=IntegerDigits[n]}, If[d[[1]] != d[[-1]], Return[False]]; MemberQ[{{},{0},{-2}}, nonz@ Differences@ Sign@ nonz@ Differences@d]]; Select[Range[1000], hillQ] (* Amiram Eldar, Dec 19 2018 *)

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A266140 Palindromes such that removing at most one digit will result in a term in A110784.

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

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A110785 Palindromes in which the digits are in nonincreasing order halfway through.

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A193408 Hill numbers.

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