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

Author

Amarnath Murthy, Aug 12 2005

Keywords

• base
• easy
• nonn

Examples

			After 191 the next term is 222 and not 202 or 212.
Terms like 101, 202, 212, 303, 313, 323, ... are not included.
		

Links

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

Crossrefs

Cf. A002113, A110785.

Programs

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 *)