cp's OEIS Frontend

A109373 Semiprimes of the form semiprime + 1.

%I A109373 #20 Jan 31 2017 16:15:39
%S A109373 10,15,22,26,34,35,39,58,86,87,94,95,119,122,123,134,142,143,146,159,
%T A109373 178,202,203,206,214,215,218,219,254,299,302,303,327,335,362,382,394,
%U A109373 395,446,447,454,482,502,515,527,538,543,554,566,623,634,635,695,698
%N A109373 Semiprimes of the form semiprime + 1.
%H A109373 Reinhard Zumkeller, <a href="/A109373/b109373.txt">Table of n, a(n) for n = 1..10000</a>
%F A109373 a(n) is in this sequence iff a(n) is in A001358 and (a(n)-1) is in A001358.
%F A109373 a(n) = A070552(n) + 1.
%e A109373 a(1) = 10 because (3*3+1)=(2*5) = 10.
%e A109373 a(2) = 15 because (2*7+1)=(3*5) = 15.
%e A109373 a(3) = 22 because (3*7+1)=(2*11) = 22.
%e A109373 a(4) = 26 because (5*5+1)=(2*13) = 26.
%e A109373 a(5) = 34 because (3*11+1)=(2*17) = 34.
%t A109373 fQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; Select[ Range[ 700], fQ[ # - 1] && fQ[ # ] &] (* _Robert G. Wilson v_ *)
%t A109373 With[{sps=Select[Range[700],PrimeOmega[#]==2&]},Transpose[Select[ Partition[ sps,2,1],#[[2]]-#[[1]]==1&]][[2]]] (* _Harvey P. Dale_, Sep 05 2012 *)
%o A109373 (Haskell)
%o A109373 a109373 n = a109373_list !! (n-1)
%o A109373 a109373_list = filter ((== 1) . a064911) a088707_list
%o A109373 -- _Reinhard Zumkeller_, Feb 20 2012
%o A109373 (PARI) is(n)=bigomega(n)==2 && bigomega(n-1)==2 \\ _Charles R Greathouse IV_, Jan 31 2017
%Y A109373 Primes are in A000040. Semiprimes are in A001358.
%Y A109373 Primes of the form semiprime + 1 are in A005385 (safe primes).
%Y A109373 Semiprimes of the form semiprime + 1 are in this sequence.
%Y A109373 3-almost primes of the form semiprime + 1 are in A109067.
%Y A109373 4-almost primes of the form semiprime + 1 are in A109287.
%Y A109373 5-almost primes of the form semiprime + 1 are in A109383.
%Y A109373 Least n-almost prime of the form semiprime + 1 are in A128665.
%Y A109373 Cf. A056809, A077065, A079148, A086005, A086006, A092307.
%Y A109373 Subsequence of A088707; A064911.
%K A109373 easy,nonn
%O A109373 1,1
%A A109373 _Jonathan Vos Post_, Aug 24 2005
%E A109373 Extended by _Ray Chandler_ and _Robert G. Wilson v_, Aug 25 2005
%E A109373 Edited by _Ray Chandler_, Mar 20 2007