

A262039


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


2



0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 11, 11, 11, 11, 11, 11, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 22, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 33, 44, 44, 44, 44, 44, 44, 44, 44, 44, 44, 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
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OFFSET

0,3


COMMENTS

In analogy to the numerical "round" function, we "round up" to the next larger palindrome A262038(n) if it is at the same distance or closer, else we "round down" to the next smaller palindrome A261423(n). See A262040 for a variant where the next smaller palindrome is chosen in case of equal distance.


LINKS



EXAMPLE

a(10) = 11 since we round up if the next smaller palindrome (here 9) is at the same distance, both 9 and 11 are here at distance 1 from n = 10.
a(16) = 11 since 16  11 = 5 is smaller than 16  22 = 6.
a(17) = 22 since 17  22 = 5 is smaller than 17  11 = 6.
a(27) = 22 since 22  27 = 5 is smaller than 27  33 = 6.
a(28) = 33 since 33  28 = 5 is smaller than 22  28 = 6, and so on.
a(100) = 101 because we round up again in this case, where 99 and 101 both are at distance 1 from n = 100.


MATHEMATICA

palQ[n_] := Block[{d = IntegerDigits@ n}, d == Reverse@ d];
f[n_] := Block[{k = n}, While[Nand[palQ@ k, k > 1], k]; k];
g[n_] := Block[{k = n}, While[! palQ@ k, k++]; k];
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 *)


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



