A064900 Semiprimes p1*p2 such that p2 > p1 and p2 mod p1 = 2.

15, 33, 35, 51, 69, 85, 87, 123, 141, 143, 159, 161, 177, 185, 213, 235, 249, 259, 267, 303, 321, 323, 335, 339, 393, 411, 447, 485, 501, 519, 533, 535, 537, 553, 573, 591, 635, 681, 685, 699, 717, 749, 753, 771, 785, 789, 807, 835, 843, 869, 871, 879, 899

Offset: 1

Author

Patrick De Geest, Oct 13 2001

Keywords

• nonn

Links

• John Cerkan, Table of n, a(n) for n = 1..10000

Crossrefs

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

Programs

Mathematica

okQ[n_] := Module[{p, e}, {p, e} = Transpose[FactorInteger[n]]; e == {1, 1} && Mod[p[[2]], p[[1]]] == 2]; Select[Range[1000], okQ]
Select[Range[1000],PrimeOmega[#]==2&&Mod[FactorInteger[#][[;;,1]][[2]],FactorInteger[#][[;;,1]][[1]]]==2&]//Quiet (* Harvey P. Dale, Jan 09 2025 *)

PARI

isok(n) = (bigomega(n)==2) && (f=factor(n)) && (#f~ == 2) && ((f[2,1] % f[1,1]) == 2); \\ Michel Marcus, May 20 2017

Extensions

Name clarified by Sean A. Irvine, Jul 31 2023