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

%I A110784 #17 Jul 31 2025 10:56:48
%S A110784 1,2,3,4,5,6,7,8,9,11,22,33,44,55,66,77,88,99,111,121,131,141,151,161,
%T A110784 171,181,191,222,232,242,252,262,272,282,292,333,343,353,363,373,383,
%U A110784 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
%N A110784 Palindromes in which the digits are in nondecreasing order halfway through.
%H A110784 Paolo Xausa, <a href="/A110784/b110784.txt">Table of n, a(n) for n = 1..1000</a>
%e A110784 After 191 the next term is 222 and not 202 or 212.
%e A110784 Terms like 101, 202, 212, 303, 313, 323, ... are not included.
%p A110784 isA110784 := proc(n::integer)
%p A110784     if isA002113(n) then # use code in A002113
%p A110784         dgs := convert(n,base,10) ;
%p A110784         for d from 2 to ceil(nops(dgs)/2) do
%p A110784             if op(d,dgs) < op(d-1,dgs) then
%p A110784                 return false;
%p A110784             end if;
%p A110784         end do:
%p A110784         true ;
%p A110784     else
%p A110784         false;
%p A110784     end if;
%p A110784 end proc:
%p A110784 for n from 1 to 3000 do
%p A110784     if isA110784(n) then
%p A110784         printf("%d,",n);
%p A110784     end if;
%p A110784 end do: # _R. J. Mathar_, Jul 30 2025
%t A110784 A110784Q[k_] := PalindromeQ[#] && Min[Differences[#[[;;Ceiling[Length[#]/2]]]]] >= 0 & [IntegerDigits[k]];
%t A110784 Select[Range[2000], A110784Q] (* _Paolo Xausa_, Jul 31 2025 *)
%Y A110784 Cf. A002113, A110785.
%K A110784 base,easy,nonn
%O A110784 1,2
%A A110784 _Amarnath Murthy_, Aug 12 2005