A047813 Largest palindromic substring of n.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 11, 2, 3, 4, 5, 6, 7, 8, 9, 2, 2, 22, 3, 4, 5, 6, 7, 8, 9, 3, 3, 3, 33, 4, 5, 6, 7, 8, 9, 4, 4, 4, 4, 44, 5, 6, 7, 8, 9, 5, 5, 5, 5, 5, 55, 6, 7, 8, 9, 6, 6, 6, 6, 6, 6, 66, 7, 8, 9, 7, 7, 7, 7, 7, 7, 7, 77, 8, 9, 8, 8, 8, 8, 8, 8, 8, 8, 88, 9, 9, 9, 9, 9, 9, 9

Offset

0,3

Comments

a(n) = A262188(n,A262190(n)-1). - Reinhard Zumkeller, Sep 14 2015

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Index entries for sequences related to palindromes

Example

a(1313) = Max{1,3,131,313} = 313.

Mathematica

palQ[n_Integer, base_Integer] := Module[{idn = IntegerDigits[n, base]}, idn == Reverse[ idn]]; f[n_] := Block[{id = IntegerDigits@ n, mx = -Infinity}, k = Length@ id; While[k > 0 && mx == -Infinity, mx = Max[mx, Select[ FromDigits@# & /@ Partition[id, k, 1], palQ[#, 10] &]]; k--]; mx] (* Robert G. Wilson v, Aug 24 2011 *)
lps[n_]:=Module[{idn=IntegerDigits[n]}, Max[FromDigits/@Select[ Flatten[ Table[ Partition[ idn, i, 1], {i, Length[idn]}], 1], #==Reverse[#]&]]]; Array[ lps, 100, 0] (* Harvey P. Dale, Jan 09 2015 *)

Prog

(Haskell)
a047813 = last . a262188_row
-- Reinhard Zumkeller, Sep 14 2015, Aug 23 2011
(Python)
def c(s): return (s[0] != "0" or s == "0") and s == s[::-1]
def a(n):
    s = str(n)
    ss = (s[i:j] for i in range(len(s)) for j in range(i+1, len(s)+1))
    return max(int(w) for w in ss if c(w))
print([a(n) for n in range(96)]) # Michael S. Branicky, Sep 18 2022

Crossrefs

Cf. A136522.

Cf. A262188, A262223, A262224.

Sequence in context: A179933 A259433 A344487 * A084051 A069652 A055483

Adjacent sequences: A047810 A047811 A047812 * A047814 A047815 A047816

Keyword

nonn,easy,base,nice,look

Author

N. J. A. Sloane

Status

approved