A086005 Semiprimes sandwiched between semiprimes.

34, 86, 94, 122, 142, 202, 214, 218, 302, 394, 446, 634, 698, 842, 922, 1042, 1138, 1262, 1346, 1402, 1642, 1762, 1838, 1894, 1942, 1982, 2102, 2182, 2218, 2306, 2362, 2434, 2462, 2518, 2642, 2722, 2734, 3098, 3386, 3602, 3694, 3866, 3902, 3958, 4286, 4414

Offset

1,1

Comments

These are some of the balanced semiprimes (see A213025). - Alonso del Arte, Jun 04 2012

Links

T. D. Noe, Table of n, a(n) for n=1..10000

Eric Weisstein's World of Mathematics, Semiprime

Formula

a(n) = 2*A086006(n).

a(n) = A056809(n)+1. - Zak Seidov, Sep 30 2012

Example

94 = 47*2: 94 - 1 = 3*31 and 94 + 1 = 5*19, therefore 94 is in the sequence.

Mathematica

u[n_]:=Plus@@Last/@FactorInteger[n]==2; lst={}; Do[If[u[n], sp=n; If[u[sp-1]&&u[sp+1], AppendTo[lst, sp]]], {n, 8!}]; lst  (* Vladimir Joseph Stephan Orlovsky, Nov 16 2009 *)
(* First run program for A109611 to define semiPrimeQ *) Select[Range[4000], Union[{semiPrimeQ[# - 1], semiPrimeQ[#], semiPrimeQ[# + 1]}] == {True} &] (* Alonso del Arte, Jun 03 2012 *)
Select[Partition[Range@ 4000, 3, 1], Union@ PrimeOmega@ # == {2} &][[All, 2]] (* Michael De Vlieger, Jun 14 2017 *)

Prog

(Haskell)
a086005 n = a086005_list !! (n-1)
a086005_list = filter
   (\x -> a064911 (x - 1) == 1 && a064911 (x + 1) == 1) a100484_list
-- Reinhard Zumkeller, Aug 08 2013, Jun 10 2012
(Python)
from itertools import count, islice
from sympy import factorint, isprime
def agen(): # generator of terms
    nxt = 0
    for k in count(2, 2):
        prv, nxt = nxt, sum(factorint(k+1).values())
        if prv == nxt == 2 and isprime(k//2): yield k
print(list(islice(agen(), 46))) # Michael S. Branicky, Nov 26 2022

Crossrefs

Cf. A001358, A056809, A064911, A100484, A123255.

Sequence in context: A278311 A213025 A365200 * A169834 A248201 A140602

Adjacent sequences: A086002 A086003 A086004 * A086006 A086007 A086008

Keyword

nonn

Author

Reinhard Zumkeller, Jul 07 2003

Status

approved