A329267 a(n) is the absolute difference between n and its nearest palindromic neighbor.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2, 1, 0, 1, 2, 3, 4, 5, 5, 4, 3, 2

Offset

0,14

Comments

Empirical observation: this sequence is similar to A261424 but yields the absolute difference between n and its nearest palindromic neighbor. It answers the question "How far from this number is the nearest palindrome?"

Links

Table of n, a(n) for n=0..86.

Index entries for sequences related to distance to nearest element of some set

Example

For 0 <= n <= 9, n is palindromic so a(n) = 0.
a(10) = 10-9 = 11-10 = 1 (10 is equidistant from its two nearest palindromes).
a(11) = 0 because 11 is palindromic.
For 12 <= n <= 16, a(n) = n-11 because 11 is the nearest palindromic number.
For 17 <= n <= 22, a(n) = 22-n because 22 is the nearest palindromic number.
.
   n  nearest palindrome  difference
  --  ------------------  ----------
   1           1            1-1 = 0
   2           2            2-2 = 0
   3           3            3-3 = 0
   4           4            4-4 = 0
   5           5            5-5 = 0
   6           6            6-6 = 0
   7           7            7-7 = 0
   8           8            8-8 = 0
   9           9            9-9 = 0
  10        9 or 11     10-9 = 11-10 = 1
  11          11           11-11 = 0
  12          11           12-11 = 1
  13          11           13-11 = 2
  14          11           14-11 = 3
  15          11           15-11 = 4
  16          11           16-11 = 5
  17          22           22-17 = 5
  18          22           22-18 = 4
  19          22           22-19 = 3
  20          22           22-20 = 2
  21          22           22-21 = 1
  22          22           22-22 = 0
  23          22           23-22 = 1

Mathematica

palQ[n_] := Block[{d = IntegerDigits[n]}, d == Reverse@ d]; a[n_] := Block[{k=0}, While[! palQ[n+k] && ! palQ[n-k], k++]; k]; Array[a, 121] (* Giovanni Resta, Nov 12 2019 *)

Prog

(PARI) ispal(n) = my (d=digits(n)); d==Vecrev(d)
a(n) = for (k=0, oo, if (ispal(n-k) || ispal(n+k), return (k))) \\ Rémy Sigrist, Dec 03 2019

Crossrefs

Cf. A261424, A261423.

Sequence in context: A301534 A101916 A361979 * A100771 A234470 A113771

Adjacent sequences: A329264 A329265 A329266 * A329268 A329269 A329270

Keyword

nonn,base

Author

Christopher J. Shore, Nov 09 2019

Status

approved