A216302 Numbers k such that 10k+9 is composite but 10k+1, 10k+3, 10k+7 are all prime.

4, 31, 46, 64, 88, 109, 130, 367, 400, 493, 523, 550, 823, 829, 886, 946, 1033, 1117, 1369, 1390, 1408, 1432, 1825, 1999, 2161, 2329, 2356, 2374, 2503, 2626, 2668, 2671, 2794, 2902, 3049, 3139, 3151, 3154, 3232, 3253, 3421, 3553, 3559, 3601, 3799, 3904

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 + 7}, AppendTo[t, n]], {n, 0, 4903}]; t (* T. D. Noe, Sep 03 2012 *)
Select[Range[4000],!PrimeQ[10#+9]&&And@@PrimeQ[10#+{1,3,7}]&] (* Harvey P. Dale, May 23 2014 *)
Select[Range[4000],Boole[PrimeQ[10 #+{1,3,7,9}]]=={1,1,1,0}&] (* Harvey P. Dale, Feb 14 2025 *)

Formula

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