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

1,1

Links

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

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.

Example

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.

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 *)

Prog

(Haskell)
a109373 n = a109373_list !! (n-1)
a109373_list = filter ((== 1) . a064911) a088707_list
-- Reinhard Zumkeller, Feb 20 2012
(PARI) is(n)=bigomega(n)==2 && bigomega(n-1)==2 \\ Charles R Greathouse IV, Jan 31 2017

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.

Sequence in context: A075523 A115679 A337610 * A373421 A267329 A120138

Adjacent sequences: A109370 A109371 A109372 * A109374 A109375 A109376

Keyword

easy,nonn

Author

Jonathan Vos Post, Aug 24 2005

Extensions

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

Edited by Ray Chandler, Mar 20 2007

Status

approved