A166580 Prime numbers containing the string 222.

2221, 12227, 22229, 22247, 22259, 22271, 22273, 22277, 22279, 22283, 22291, 42221, 42223, 42227, 52223, 72221, 72223, 72227, 72229, 82223, 92221, 92227, 102229, 112223, 122201, 122203, 122207, 122209, 122219, 122231, 122251, 122263, 122267, 122273, 122279, 122299, 132229, 142223

Offset: 1

Author

Vincenzo Librandi, Nov 01 2009

Keywords

• nonn
• base

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000

Crossrefs

Cf. A243527, A166581, A166582, A167281, A131645, A167282, A167290, A167292.

Programs

Magma

res := []; for n in [1..15000] do p := NthPrime(n); digits := IntegerToSequence(p); for i in [1..#digits - 2] do if digits[i..i+2] eq [2,2,2] then Append(~res, p); break; end if; end for; end for; res; // Vincenzo Librandi, Jul 16 2025

Mathematica

p222Q[n_] := Module[{idn = IntegerDigits[n]}, MemberQ[Partition[idn, 3, 1], {2, 2, 2}]]; Select[Prime[Range[15000]], p222Q] (* Vincenzo Librandi Sep 14 2012 *)
Select[Prime[Range[12000]],SequenceCount[IntegerDigits[#],{2,2,2}]>0&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Nov 08 2017 *)

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,222) \\ Charles R Greathouse IV, Jun 20 2014

Formula

a(n) ~ n log n. - Charles R Greathouse IV, Jun 20 2014