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 A109373 Semiprimes of the form semiprime + 1. 9

%I

%S 10,15,22,26,34,35,39,58,86,87,94,95,119,122,123,134,142,143,146,159,

%T 178,202,203,206,214,215,218,219,254,299,302,303,327,335,362,382,394,

%U 395,446,447,454,482,502,515,527,538,543,554,566,623,634,635,695,698

%N Semiprimes of the form semiprime + 1.

%H Reinhard Zumkeller, <a href="/A109373/b109373.txt">Table of n, a(n) for n = 1..10000</a>

%F a(n) is in this sequence iff a(n) is in A001358 and (a(n)-1) is in A001358.

%F a(n) = A070552(n) + 1.

%e a(1) = 10 because (3*3+1)=(2*5) = 10.

%e a(2) = 15 because (2*7+1)=(3*5) = 15.

%e a(3) = 22 because (3*7+1)=(2*11) = 22.

%e a(4) = 26 because (5*5+1)=(2*13) = 26.

%e a(5) = 34 because (3*11+1)=(2*17) = 34.

%t fQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; Select[ Range[ 700], fQ[ # - 1] && fQ[ # ] &] (* _Robert G. Wilson v_ *)

%t With[{sps=Select[Range,PrimeOmega[#]==2&]},Transpose[Select[ Partition[ sps,2,1],#[]-#[]==1&]][]] (* _Harvey P. Dale_, Sep 05 2012 *)

%o (Haskell)

%o a109373 n = a109373_list !! (n-1)

%o a109373_list = filter ((== 1) . a064911) a088707_list

%o -- _Reinhard Zumkeller_, Feb 20 2012

%o (PARI) is(n)=bigomega(n)==2 && bigomega(n-1)==2 \\ _Charles R Greathouse IV_, Jan 31 2017

%Y Primes are in A000040. Semiprimes are in A001358.

%Y Primes of the form semiprime + 1 are in A005385 (safe primes).

%Y Semiprimes of the form semiprime + 1 are in this sequence.

%Y 3-almost primes of the form semiprime + 1 are in A109067.

%Y 4-almost primes of the form semiprime + 1 are in A109287.

%Y 5-almost primes of the form semiprime + 1 are in A109383.

%Y Least n-almost prime of the form semiprime + 1 are in A128665.

%Y Cf. A056809, A077065, A079148, A086005, A086006, A092307.

%Y Subsequence of A088707; A064911.

%K easy,nonn

%O 1,1

%A _Jonathan Vos Post_, Aug 24 2005

%E Extended by _Ray Chandler_ and _Robert G. Wilson v_, Aug 25 2005

%E Edited by _Ray Chandler_, Mar 20 2007

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Last modified August 19 08:17 EDT 2019. Contains 326115 sequences. (Running on oeis4.)