A216293 Values of k such that there are exactly two primes between 10k and 10k + 9.

2, 3, 5, 6, 8, 15, 16, 17, 23, 25, 26, 27, 28, 33, 34, 35, 37, 38, 40, 44, 49, 50, 52, 54, 56, 57, 59, 60, 65, 67, 70, 73, 75, 76, 91, 94, 97, 99, 101, 110, 112, 115, 118, 121, 122, 123, 127, 128, 129, 132, 136, 143, 149, 154, 155, 157, 161, 162, 172, 174

Offset: 1

Author

V. Raman, Sep 03 2012

Keywords

• nonn

Examples

			23 is in the sequence because between 230 and 239 there are exactly two primes: 233 and 239. [_Bruno Berselli_, Sep 04 2012]
		

Links

• V. Raman, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A032352, A007811, A078494, A216292.

Programs

Magma

[n: n in [1..200] | #PrimesInInterval(10*n, 10*n+9) eq 2]; // Bruno Berselli, Sep 04 2012

Mathematica

t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[Length[ps] == 2, AppendTo[t, n]], {n, 0, 229}]; t (* T. D. Noe, Sep 03 2012 *)
Select[Range[200],Count[Range[10#,10#+9],?PrimeQ]==2&] (* _Harvey P. Dale, Jan 19 2017 *)

Formula

a(n) >> n log^2 n. - Charles R Greathouse IV, Sep 07 2012