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

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

1,2

Comments

Also, palindromic valley numbers, or palindromes in A193413. - Michael S. Branicky, Feb 01 2026

Links

Paolo Xausa, Table of n, a(n) for n = 1..1000

Example

After 111 the next term is 202 and not 121, 131, up to 191.
From Alexander Yutkin, Feb 02 2026: (Start)
Illustration using number 54332223345:
  . . . . . . . . . . .
  5 . . . . . . . . . 5
  . 4 . . . . . . . 4 .
  . . 3 3 . . . 3 3 . .
  . . . . 2 2 2 . . . .
  . . . . . . . . . . .
(End)

Mathematica

A110785Q[k_] := PalindromeQ[#] && (Length[#] <= 2 || Max[Differences[#[[;; Ceiling[Length[#]/2]]]]] <= 0) & [IntegerDigits[k]];
Select[Range[2000], A110785Q] (* Paolo Xausa, Jul 31 2025, corrected on Feb 01 2026 *)

Prog

(Python)
def ok(n): return (s:=str(n)) == s[::-1] and (h:=s[:(len(s)+1)//2]) == "".join(sorted(h, reverse=True))
print([k for k in range(1, 850) if ok(k)]) # Michael S. Branicky, Feb 01 2026

Crossrefs

Intersection of A002113 and A193413.

Cf. A193409, A134970, A110784

Sequence in context: A394545 A276354 A084982 * A193413 A087992 A062687

Adjacent sequences: A110782 A110783 A110784 * A110786 A110787 A110788

Keyword

base,easy,nonn

Author

Amarnath Murthy, Aug 12 2005

Status

approved