A047814 Largest prime substring of n, or 0 if no such substring exists.

0, 0, 2, 3, 0, 5, 0, 7, 0, 0, 0, 11, 2, 13, 0, 5, 0, 17, 0, 19, 2, 2, 2, 23, 2, 5, 2, 7, 2, 29, 3, 31, 3, 3, 3, 5, 3, 37, 3, 3, 0, 41, 2, 43, 0, 5, 0, 47, 0, 0, 5, 5, 5, 53, 5, 5, 5, 7, 5, 59, 0, 61, 2, 3, 0, 5, 0, 67, 0, 0, 7, 71, 7, 73, 7, 7, 7, 7, 7, 79, 0, 0, 2, 83, 0, 5, 0, 7, 0, 89

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy
• base
• nice
• look

Comments

A211396(n) <= a(n). - Reinhard Zumkeller, Feb 08 2013

Examples

			a(10)=0, a(1227)=227.
		

Links

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

Crossrefs

Cf. A211396.

Programs

Haskell

import Data.List (isInfixOf)
a047814 n = if null ips then 0 else head ips
   where ips = [p | p <- reverse $ takeWhile (<= n) a000040_list,
                    show p `isInfixOf` show n]
-- Reinhard Zumkeller, Feb 08 2013

Mathematica

a[n_] := (id = IntegerDigits[n]; lg = Length[id]; sel = Select[ FromDigits /@ Flatten[ Table[ id[[i ;; j]], {i, 1, lg}, {j, i, lg}], 1], PrimeQ]; If[ sel === {}, 0, Last[ Sort[ sel] ] ]); Table[ a[n], {n, 0, 99}] (* Jean-François Alcover, Feb 23 2012 *)
lps[m_]:=Max[Select[Flatten[Table[FromDigits/@Partition[ IntegerDigits[ m],n,1],{n,IntegerLength[m]}]],PrimeQ]]; Array[lps,100,0]/. -\[Infinity]->0 (* Harvey P. Dale, Feb 26 2014 *)

Extensions

Corrected (41) by Jean-François Alcover, Feb 23 2012