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A262040 Nearest palindrome to n; in case of a tie choose the smaller palindrome.

%I A262040 #11 Sep 10 2015 14:18:12
%S A262040 0,1,2,3,4,5,6,7,8,9,9,11,11,11,11,11,11,22,22,22,22,22,22,22,22,22,
%T A262040 22,22,33,33,33,33,33,33,33,33,33,33,33,44,44,44,44,44,44,44,44,44,44,
%U A262040 44,55,55,55,55,55,55,55,55,55,55,55,66,66,66,66,66,66,66,66,66,66,66,77,77
%N A262040 Nearest palindrome to n; in case of a tie choose the smaller palindrome.
%C A262040 In contrast to A262039, here we "round down" to the next smaller palindrome A261423(n) if it is at the same distance or closer, else we "round up" to the next larger palindrome A262038(n).
%e A262040 a(10) = 9 since we round down if the next larger palindrome (here 11) is at the same distance, both 9 and 11 are here at distance 1 from n = 10.
%e A262040 a(16) = 11 since |16 - 11| = 5 is smaller than |16 - 22| = 6.
%e A262040 a(17) = 22 since |17 - 22| = 5 is smaller than |17 - 11| = 6.
%e A262040 a(27) = 22 since |22 - 27| = 5 is smaller than |27 - 33| = 6.
%e A262040 a(28) = 33 since |33 - 28| = 5 is smaller than |22 - 28| = 6, and so on.
%e A262040 a(100) = 99 because we round down in this case, where 99 and 101 both are at distance 1 from n = 100.
%t A262040 palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d];
%t A262040 f[n_] := Block[{k = n}, While[Nand[palQ@ k, k > -1], k--]; k];
%t A262040 g[n_] := Block[{k = n}, While[! palQ@ k, k++]; k];
%t A262040 h[n_] := Block[{a = f@ n, b = g@ n}, Which[palQ@ n, n, (b - n) - (n - a) >= 0, a, (b - n) - (n - a) < 0, b]]; Table[h@ n, {n, 0, 73}] (* _Michael De Vlieger_, Sep 09 2015 *)
%Y A262040 Cf. A002113, A261423, A262037, A262038, A262039.
%K A262040 nonn,base
%O A262040 0,3
%A A262040 _M. F. Hasler_, Sep 08 2015