A166573 Prime numbers containing the string 13.

13, 113, 131, 137, 139, 313, 613, 1013, 1213, 1301, 1303, 1307, 1319, 1321, 1327, 1361, 1367, 1373, 1381, 1399, 1613, 1913, 2113, 2131, 2137, 2213, 2713, 3137, 3313, 3413, 3613, 4013, 4133, 4139, 4513, 4813, 5113, 5413, 5813, 6113, 6131, 6133, 7013, 7213, 8513

Offset: 1

Author

Vincenzo Librandi, Nov 01 2009

Keywords

• nonn
• base

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Triskaidekaphobia
• Wikipedia, Triskaidekaphobia

Crossrefs

Complement of A076805 with respect to A000040.

Cf. A166571, A166572, A166579, A166580, A166581, A166582.

Programs

Haskell

import Data.List (isInfixOf)
a166573 n = a166573_list !! (n-1)
a166573_list = filter (("13" `isInfixOf`) . show) a000040_list
-- Reinhard Zumkeller, Nov 09 2011

Mathematica

p13Q[n_] := Module[{idn = IntegerDigits[n]}, MemberQ[Partition[idn, 2, 1], {1, 3}]]; Select[Prime[Range[1000]], p13Q] (* Vincenzo Librandi, Sep 14 2012 *)
Select[Prime[Range[1500]], ! StringFreeQ[ToString[#], "13"] &] (* Vincenzo Librandi, May 03 2015 *)

PARI

contains(n,k)=my(N=digits(n),K=digits(k)); for(i=0,#N-#K, for(j=1,#K,if(N[i+j]!=K[j],next(2))); return(1)); 0
is(n)=isprime(n) && contains(n,13) \\ Charles R Greathouse IV, Jun 20 2014

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Nov 09 2011

Extensions

Corrected (313 inserted) by R. J. Mathar, Nov 30 2009