A243527 Prime numbers containing the string 111.

1117, 2111, 4111, 8111, 10111, 11113, 11117, 11119, 11131, 11149, 11159, 11161, 11171, 11173, 11177, 11197, 16111, 22111, 25111, 26111, 28111, 35111, 40111, 41113, 41117, 44111, 47111, 50111, 58111, 65111, 68111, 70111, 71119, 79111, 80111

Offset: 1

Author

Vincenzo Librandi, Jun 06 2014

Keywords

• nonn
• base
• easy

Links

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

Crossrefs

Cf. prime numbers containing the string kkk: this sequence (k=1), A166580 (k=2), A166581 (k=3), A166582 (k=4), A167281 (k=5), A131645 (k=6), A167282 (k=7), A167290 (k=8), A167292 (k=9).

Programs

Mathematica

Select[Prime[Range[90000]], !StringFreeQ[ToString[#], "111"]&]

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

Formula

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