A166572 Prime numbers containing the string 11.

11, 113, 211, 311, 811, 911, 1103, 1109, 1117, 1123, 1129, 1151, 1153, 1163, 1171, 1181, 1187, 1193, 1511, 1811, 2011, 2111, 2113, 2311, 2411, 2711, 3011, 3119, 3511, 3911, 4111, 4211, 5011, 5113, 5119, 5711, 6011, 6113, 6211, 6311, 6911, 7211, 7411

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. A166571, A166573, A166579, A166580, A166581, A166582.

Programs

Maple

isA166572 := proc(n) local dgs,wrks; if isprime(n) then dgs := convert(n,base,10) ; wrks := false; for i from 1 to nops(dgs)-1 do if op(i,dgs) = 1 and op(i+1,dgs) = 1 then return true; end if; od: return false; else false; end if; end proc: for n from 1 to 8000 do if isA166572(n) then printf("%d,",n) ; end if; od: # R. J. Mathar, Nov 30 2009

Mathematica

p11Q[n_]: = Module[{idn = IntegerDigits[n]}, MemberQ[Partition[idn, 2, 1], {1, 1}]] Select[Prime[Range[1000]], p11Q] (* Vincenzo Librandi, Sep 14 2012 *)
Select[Prime[Range[1000]],SequenceCount[IntegerDigits[#],{1,1}]>0&] (* Harvey P. Dale, Sep 24 2022 *)

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

Formula

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