A110785 -id:A110785 - cp's OEIS frontend

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

Amarnath Murthy, Aug 12 2005

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

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

Cf. A002113, A110785.

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

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

A193413 Valley numbers.

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, 858, 868, 878, 888, 909, 919, 929, 939, 949, 959, 969, 979, 989, 999, 1001

Offset: 1

Jaroslav Krizek, Jul 25 2011

For n > 10 the structure of digits represents a valley. The first digit is equal to the last digit (1 - 9). The first digits are in nonincreasing order. The last digits are in nondecreasing order. The numbers may have more than one smallest digit. Sequence is infinite.
Superset of crater numbers (A193409) and A193412.
See valley numbers in base 2 (A193414 and A193415).

			Illustration using 6543333346:
  6 . . . . . . . . 6
  . 5 . . . . . . . .
  . . 4 . . . . . 4 .
  . . . 3 3 3 3 3 . .

Cf. A110785, A193409, A193412, A193414, A193415.

Cf. A134970. - Omar E. Pol, Aug 05 2011

More terms extended by definition by Jaroslav Krizek, Jul 27 2011

cp's OEIS Frontend

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

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