A216300 Numbers k such that 10k+3 is composite but 10k+1, 10k+7, 10k+9 are all prime.

13, 160, 376, 391, 421, 547, 586, 712, 745, 748, 754, 808, 883, 985, 1006, 1210, 1291, 1333, 1375, 1462, 1513, 1588, 1702, 1798, 2203, 2269, 2302, 2353, 2497, 2584, 2854, 2920, 3205, 3358, 3436, 3583, 3823, 3832, 3856, 3982, 4003, 4084, 4138, 4339, 4402

Offset: 1

Author

V. Raman, Sep 03 2012

Keywords

• nonn

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 + 7, 10*n + 9}, AppendTo[t, n]], {n, 0, 4738}]; t (* T. D. Noe, Sep 03 2012 *)
Select[Range[5000],Boole[PrimeQ[10 #+{1,3,7,9}]]=={1,0,1,1}&] (* Harvey P. Dale, Jan 29 2025 *)

Formula

a(n) >> n log^3 n. - Charles R Greathouse IV, Sep 07 2012