A110784 Palindromes in which the digits are in nondecreasing order halfway through.

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, 1331, 1441, 1551, 1661, 1771, 1881, 1991, 2222

Offset

1,2

Comments

Also palindromic hill numbers. - Alexander Yutkin, Feb 02 2026

Links

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

Example

After 191 the next term is 222 and not 202 or 212.
Terms like 101, 202, 212, 303, 313, 323, ... are not included.
From Alexander Yutkin, Feb 02 2026: (Start)
Illustration using number 233555332:
  . . . . . . . . .
  . . . 5 5 5 . . .
  . . . . . . . . .
  . 3 3 . . . 3 3 .
  2 . . . . . . . 2
  . . . . . . . . .
(End)

Maple

isA110784 := proc(n::integer)
    if isA002113(n) then # use code in A002113
        dgs := convert(n, base, 10) ;
        for d from 2 to ceil(nops(dgs)/2) do
            if op(d, dgs) < op(d-1, dgs) then
                return false;
            end if;
        end do:
        true ;
    else
        false;
    end if;
end proc:
for n from 1 to 3000 do
    if isA110784(n) then
        printf("%d, ", n);
    end if;
end do: # R. J. Mathar, Jul 30 2025

Mathematica

A110784Q[k_] := PalindromeQ[#] && Min[Differences[#[[;; Ceiling[Length[#]/2]]]]] >= 0 & [IntegerDigits[k]];
Select[Range[2000], A110784Q] (* Paolo Xausa, Jul 31 2025 *)

Prog

(Python)
def ok(n): return (s:=str(n)) == s[::-1] and (h:=s[:(len(s)+1)//2]) == "".join(sorted(h))
print([k for k in range(1, 2223) if ok(k)]) # Michael S. Branicky, Feb 01 2026

Crossrefs

Intersection of A002113 and A193408.

Cf. A134810, A134941, A110785.

Sequence in context: A295010 A257054 A193408 * A395936 A368944 A346217

Adjacent sequences: A110781 A110782 A110783 * A110785 A110786 A110787

Keyword

base,easy,nonn

Author

Amarnath Murthy, Aug 12 2005

Status

approved