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

1,1

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Triskaidekaphobia

Wikipedia, Triskaidekaphobia

Formula

a(n) ~ n log n. - Charles R Greathouse IV, 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 *)

Prog

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

Crossrefs

Complement of A076805 with respect to A000040.

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

Sequence in context: A302307 A293873 A044345 * A044726 A303038 A141937

Adjacent sequences: A166570 A166571 A166572 * A166574 A166575 A166576

Keyword

nonn,base

Author

Vincenzo Librandi, Nov 01 2009

Extensions

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

Status

approved