login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A278311 A213025 A365200 * A169834 A248201 A140602
KEYWORD
nonn
AUTHOR
Reinhard Zumkeller, Jul 07 2003
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 19 06:05 EDT 2024. Contains 370952 sequences. (Running on oeis4.)