A216303 Numbers k such that 10k+1 and 10k+3 are prime but 10k+7 and 10k+9 are composite.

28, 52, 115, 172, 193, 211, 214, 259, 280, 337, 358, 382, 385, 424, 427, 442, 448, 502, 613, 655, 676, 679, 733, 901, 928, 1027, 1030, 1135, 1207, 1216, 1225, 1393, 1456, 1459, 1558, 1597, 1645, 1663, 1690, 1768, 1813, 1831, 1852, 1918, 1954, 1984, 1996, 2023

Offset: 1

Author

V. Raman, Sep 03 2012

Keywords

• nonn

Examples

			28 is a member since 281 & 283 are prime while 287 & 289 are composite.
		

Links

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

Crossrefs

Cf. A032352, A007811, A078494.

Programs

Mathematica

t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[ps == {10*n + 1, 10*n + 3}, AppendTo[t, n]], {n, 0, 2689}]; t (* T. D. Noe, Sep 04 2012 *)
Select[Range[2100],PrimeQ[10#+{1,3,7,9}]=={True,True,False,False}&] (* Harvey P. Dale, Dec 17 2014 *)

Formula

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

Extensions

Definition corrected by Harvey P. Dale, Dec 17 2014