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

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, 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

Offset

0,3

Comments

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).

Links

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

Example

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.
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) = 99 because we round down 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, A262039.

Sequence in context: A262087 A261914 A261423 * A329200 A122638 A297235

Adjacent sequences: A262037 A262038 A262039 * A262041 A262042 A262043

Keyword

nonn,base

Author

M. F. Hasler, Sep 08 2015

Status

approved