A064905 Semiprimes p1*p2 such that p2>p1 and p2 mod p1 = 7.

319, 697, 767, 803, 1219, 1529, 1577, 1781, 1853, 2119, 2497, 2981, 3133, 3223, 3587, 3649, 3707, 3743, 3809, 3949, 4061, 4393, 4747, 5161, 5249, 5321, 5401, 5837, 5899, 5909, 5983, 5989, 6127, 6509, 6611, 6631, 6931, 7633, 7697, 8063, 8203, 8473, 8797, 8879

Offset: 1

Author

Patrick De Geest, Oct 13 2001

Keywords

• nonn

Links

• Harvey P. Dale, Table of n, a(n) for n = 1..1000 (corrected by Sean A. Irvine)

Crossrefs

Cf. A001358 (p2 mod p1 = 0), A064899-A064911.

Programs

Mathematica

m7Q[n_]:=Module[{f=Transpose[FactorInteger[n]][[1]]},Length[f]==2 && Mod[ f[[2]],f[[1]]]==7]; Select[Range[10000], And[m7Q[#], SquareFreeQ[#]] &] (* Harvey P. Dale, May 02 2016; corrected by Michael De Vlieger, Jul 31 2023  *)
nn = 8900; m = 7; Union@ Flatten@ Table[p = Prime[i]; Table[q = Prime[j]; If[Mod[q, p] == m, p q, Nothing], {j, i + 1, PrimePi[nn/p]}], {i, PrimePi[nn]}] (* Michael De Vlieger, Jul 31 2023 *)

Extensions

Corrected and extended by Harvey P. Dale, May 02 2016

Original data restored, name clarified, and offset corrected by Sean A. Irvine, Jul 31 2023