login
A086005
Semiprimes sandwiched between semiprimes.
14
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
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
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 07 2003
STATUS
approved