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A086005 Semiprimes sandwiched between semiprimes.

%I A086005 #39 Feb 16 2025 08:32:50
%S A086005 34,86,94,122,142,202,214,218,302,394,446,634,698,842,922,1042,1138,
%T A086005 1262,1346,1402,1642,1762,1838,1894,1942,1982,2102,2182,2218,2306,
%U A086005 2362,2434,2462,2518,2642,2722,2734,3098,3386,3602,3694,3866,3902,3958,4286,4414
%N A086005 Semiprimes sandwiched between semiprimes.
%C A086005 These are some of the balanced semiprimes (see A213025). - _Alonso del Arte_, Jun 04 2012
%H A086005 T. D. Noe, <a href="/A086005/b086005.txt">Table of n, a(n) for n=1..10000</a>
%H A086005 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Semiprime.html">Semiprime</a>
%F A086005 a(n) = 2*A086006(n).
%F A086005 a(n) = A056809(n)+1. - _Zak Seidov_, Sep 30 2012
%e A086005 94 = 47*2: 94 - 1 = 3*31 and 94 + 1 = 5*19, therefore 94 is in the sequence.
%t A086005 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 *)
%t A086005 (* First run program for A109611 to define semiPrimeQ *) Select[Range[4000], Union[{semiPrimeQ[# - 1], semiPrimeQ[#], semiPrimeQ[# + 1]}] == {True} &] (* _Alonso del Arte_, Jun 03 2012 *)
%t A086005 Select[Partition[Range@ 4000, 3, 1], Union@ PrimeOmega@ # == {2} &][[All, 2]] (* _Michael De Vlieger_, Jun 14 2017 *)
%o A086005 (Haskell)
%o A086005 a086005 n = a086005_list !! (n-1)
%o A086005 a086005_list = filter
%o A086005    (\x -> a064911 (x - 1) == 1 && a064911 (x + 1) == 1) a100484_list
%o A086005 -- _Reinhard Zumkeller_, Aug 08 2013, Jun 10 2012
%o A086005 (Python)
%o A086005 from itertools import count, islice
%o A086005 from sympy import factorint, isprime
%o A086005 def agen(): # generator of terms
%o A086005     nxt = 0
%o A086005     for k in count(2, 2):
%o A086005         prv, nxt = nxt, sum(factorint(k+1).values())
%o A086005         if prv == nxt == 2 and isprime(k//2): yield k
%o A086005 print(list(islice(agen(), 46))) # _Michael S. Branicky_, Nov 26 2022
%Y A086005 Cf. A001358, A056809, A064911, A100484, A123255.
%K A086005 nonn
%O A086005 1,1
%A A086005 _Reinhard Zumkeller_, Jul 07 2003