A193227 Semiprimes p*q such that p+1 and q+1 are semiprimes.

9, 15, 25, 39, 65, 111, 169, 183, 185, 219, 305, 365, 471, 481, 579, 785, 793, 831, 939, 949, 965, 1191, 1263, 1369, 1371, 1385, 1565, 1623, 1839, 1983, 1985, 2019, 2041, 2105, 2199, 2257, 2271, 2285, 2509, 2631, 2701, 2705, 2991

Offset

1,1

Comments

Numbers of the form A005383(i)*A005383(j) for i,j >= 1. - Altug Alkan, Mar 22 2018

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

1371 is in the sequence because 1371 = 3 * 457, and 3 + 1 = 4 and 457 + 1 = 2 * 229 are semiprimes.

Maple

with(numtheory):for n from 2 to 3000 do: x:=factorset(n):y:=bigomega(n):z:=x[1]:zz:=n/z:if y=2 and type(z, prime)=true and type(zz, prime) = true and bigomega(z+1)=2 and bigomega(zz+1)=2 then printf(`%d, `, n): else fi:od:
# Alternate:
N:= 10000: # to get all terms <= N
P:= select(p -> isprime(p) and numtheory:-bigomega(p+1)=2, [$1..N/3]):
nP:= nops(P):
sort(select(`<=`, [seq(seq(P[i]*P[j], i=1..j), j=1..nP)], N)); # Robert Israel, Mar 22 2018

Mathematica

Take[Sort[Times@@@Select[Flatten[Table[{Prime[p], Prime[q]}, {p, 2, 200}, {q, p}], 1], PrimeOmega[#[[1]] + 1] == 2 && PrimeOmega[#[[2]] + 1] == 2 &]], 45] (* Alonso del Arte, Jul 18 2011 *)
cQ[n_]:=Module[{fi=FactorInteger[n]}, Which[PrimeOmega[n]==2&&IntegerQ[Sqrt[ n]], PrimeOmega[ Sqrt[n]+1]==2, PrimeOmega[n] == 2, PrimeOmega[ 1+ fi[[All, 1]]] =={2, 2}, True, False]]; Select[Range[3000], cQ]

Prog

(PARI) list(lim)=my(v=List(), u=List(), t); forprime(p=3, lim\3, if(isprime((p+1)/2), listput(v, p))); for(i=1, #v, for(j=i, #v, t=v[i]*v[j]; if(t>lim, break); listput(u, t))); vecsort(Vec(u)) \\ Charles R Greathouse IV, Jul 18 2011

Crossrefs

Subsequence of A001358.

Cf. A005383, A193165.

Sequence in context: A342418 A251415 A109888 * A014003 A333788 A082549

Adjacent sequences: A193224 A193225 A193226 * A193228 A193229 A193230

Keyword

nonn

Author

Michel Lagneau, Jul 18 2011

Status

approved