A227129 Semiprimes n = p*q, p<q, such that both numbers n + p - 1 and n + q - 1 are prime.

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

1,1

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.

Formula

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

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 *)

Crossrefs

Cf. A006881, A226770.

Sequence in context: A075928 A020214 A127643 * A238574 A333314 A238575

Adjacent sequences: A227126 A227127 A227128 * A227130 A227131 A227132

Keyword

nonn

Author

Vladimir Shevelev, Jul 02 2013

Status

approved