A227129 Semiprimes n = p*q, p

15, 51, 85, 91, 133, 145, 235, 249, 265, 427, 451, 493, 519, 559, 565, 589, 591, 681, 721, 871, 879, 1003, 1149, 1177, 1189, 1207, 1411, 1441, 1509, 1561, 1603, 1651, 1837, 1945, 2059, 2071, 2119, 2227, 2335, 2391, 2419, 2599, 2661, 2827, 2869, 2965, 2995

Offset: 1

Author

Vladimir Shevelev, Jul 02 2013

Keywords

• nonn

Comments

Subsequence of A006881.

Links

• Peter J. C. Moses, Table of n, a(n) for n = 1..5000
• Since 591 = 3*197 and numbers 591 + 3 - 1 = 593, 591 + 197 - 1 = 787 are both primes, then 591 is in the sequence.

Crossrefs

Cf. A006881, A226770.

Programs

Mathematica

Select[Range[10000],(Last[#2]=={1,1}&&And@@PrimeQ[#1+First[#2]-1]&)[#1,Transpose[FactorInteger[#1]]]&] (* Peter J. C. Moses, Jul 03 2013 *)
spQ[n_]:=Module[{fi=Transpose[FactorInteger[n]]},fi[[2]]=={1,1}&&AllTrue[ n-1+fi[[1]],PrimeQ]]; Select[Range[3000],spQ] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 24 2015 *)

Formula

A226770(a(n)-1) = 2.