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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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=0..73.

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

Cf. A002113, A261423, A262037, A262038, A262040.

Sequence in context: A065650 A065649 A262037 * A123241 A033862 A262038

Adjacent sequences:  A262036 A262037 A262038 * A262040 A262041 A262042

KEYWORD

nonn,base

AUTHOR

M. F. Hasler, Sep 08 2015

STATUS

approved

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Last modified February 20 22:51 EST 2019. Contains 320362 sequences. (Running on oeis4.)