A216301 Numbers k such that 10k+7 is composite but 10k+1, 10k+3, 10k+9 are all prime.

7, 43, 103, 106, 145, 238, 271, 409, 472, 544, 574, 670, 721, 904, 934, 1009, 1183, 1204, 1261, 1282, 1372, 1636, 1669, 1729, 1792, 1921, 1975, 2002, 2149, 2152, 2254, 2320, 2437, 2560, 2593, 2611, 2695, 2779, 2857, 2866, 2875, 3085, 3115, 3118, 3256

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 + 3, 10*n + 9}, AppendTo[t, n]], {n, 0, 4999}]; t (* T. D. Noe, Sep 03 2012 *)
cprQ[n_]:=Module[{c=10n},!PrimeQ[c+7]&&And@@PrimeQ[c+{1,3,9}]]; Select[ Range[ 4000],cprQ] (* Harvey P. Dale, May 28 2014 *)
Select[Range[4000],Boole[PrimeQ[10 #+{1,3,7,9}]]=={1,1,0,1}&] (* Harvey P. Dale, Dec 09 2022 *)

Formula

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