A166573 - OEIS

%I #31 Feb 16 2025 08:33:11

%S 13,113,131,137,139,313,613,1013,1213,1301,1303,1307,1319,1321,1327,

%T 1361,1367,1373,1381,1399,1613,1913,2113,2131,2137,2213,2713,3137,

%U 3313,3413,3613,4013,4133,4139,4513,4813,5113,5413,5813,6113,6131,6133,7013,7213,8513

%N Prime numbers containing the string 13.

%H Reinhard Zumkeller, <a href="/A166573/b166573.txt">Table of n, a(n) for n = 1..10000</a>

%H Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Triskaidekaphobia.html">Triskaidekaphobia</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Triskaidekaphobia">Triskaidekaphobia</a>

%F a(n) ~ n log n. - _Charles R Greathouse IV_, Nov 09 2011

%t p13Q[n_] := Module[{idn = IntegerDigits[n]}, MemberQ[Partition[idn, 2, 1], {1, 3}]]; Select[Prime[Range[1000]], p13Q] (* _Vincenzo Librandi_, Sep 14 2012 *)

%t Select[Prime[Range[1500]], ! StringFreeQ[ToString[#], "13"] &] (* _Vincenzo Librandi_, May 03 2015 *)

%o (Haskell)

%o import Data.List (isInfixOf)

%o a166573 n = a166573_list !! (n-1)

%o a166573_list = filter (("13" `isInfixOf`) . show) a000040_list

%o -- _Reinhard Zumkeller_, Nov 09 2011

%o (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

%o is(n)=isprime(n) && contains(n,13) \\ _Charles R Greathouse IV_, Jun 20 2014

%Y Complement of A076805 with respect to A000040.

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

%K nonn,base,changed

%O 1,1

%A _Vincenzo Librandi_, Nov 01 2009

%E Corrected (313 inserted) by _R. J. Mathar_, Nov 30 2009