A109373 Semiprimes of the form semiprime + 1.

10, 15, 22, 26, 34, 35, 39, 58, 86, 87, 94, 95, 119, 122, 123, 134, 142, 143, 146, 159, 178, 202, 203, 206, 214, 215, 218, 219, 254, 299, 302, 303, 327, 335, 362, 382, 394, 395, 446, 447, 454, 482, 502, 515, 527, 538, 543, 554, 566, 623, 634, 635, 695, 698

Offset: 1

Author

Jonathan Vos Post, Aug 24 2005

Keywords

• easy
• nonn

Examples

			a(1) = 10 because (3*3+1)=(2*5) = 10.
a(2) = 15 because (2*7+1)=(3*5) = 15.
a(3) = 22 because (3*7+1)=(2*11) = 22.
a(4) = 26 because (5*5+1)=(2*13) = 26.
a(5) = 34 because (3*11+1)=(2*17) = 34.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Primes are in A000040. Semiprimes are in A001358.

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

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

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

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

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

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

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

Subsequence of A088707; A064911.

Programs

Haskell

a109373 n = a109373_list !! (n-1)
a109373_list = filter ((== 1) . a064911) a088707_list
-- Reinhard Zumkeller, Feb 20 2012

Mathematica

fQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; Select[ Range[ 700], fQ[ # - 1] && fQ[ # ] &] (* Robert G. Wilson v *)
With[{sps=Select[Range[700],PrimeOmega[#]==2&]},Transpose[Select[ Partition[ sps,2,1],#[[2]]-#[[1]]==1&]][[2]]] (* Harvey P. Dale, Sep 05 2012 *)

PARI

is(n)=bigomega(n)==2 && bigomega(n-1)==2 \\ Charles R Greathouse IV, Jan 31 2017

Formula

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

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

Extensions

Extended by Ray Chandler and Robert G. Wilson v, Aug 25 2005

Edited by Ray Chandler, Mar 20 2007