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

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• base
• nice
• look

Comments

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

Examples

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

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• Index entries for sequences related to palindromes

Crossrefs

Cf. A136522.

Cf. A262188, A262223, A262224.

Programs

Haskell

a047813 = last . a262188_row
-- Reinhard Zumkeller, Sep 14 2015, Aug 23 2011

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 *)

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