A092207 Semiprimes k such that k+2 is also a semiprime.

4, 33, 49, 55, 85, 91, 93, 119, 121, 141, 143, 159, 183, 185, 201, 203, 213, 215, 217, 219, 235, 247, 265, 287, 289, 299, 301, 303, 319, 321, 327, 339, 391, 393, 411, 413, 415, 445, 451, 469, 471, 515, 517, 527, 533, 535, 543, 551, 579, 581, 589, 633, 667

Offset: 1

Author

Robert G. Wilson v and Zak Seidov, Feb 24 2004

Keywords

• nonn

Comments

Starting with 33 all terms are odd. First squares are 4, 49, 169, 361, 529, 961, 1369, 2209, 2809, 4489, ... - Zak Seidov, Feb 17 2017

Links

• Zak Seidov, Table of n, a(n) for n = 1..10000
• Eric Weisstein's World of Mathematics, Semiprime

Crossrefs

Cf. A056809, A070552, A092125, A092126, A092127, A092128, A092129, A082919, A092209.

Programs

Mathematica

PrimeFactorExponentsAdded[n_] := Plus @@ Flatten[Table[ #[[2]], {1}] & /@ FactorInteger[n]]; Select[ Range[ 668], PrimeFactorExponentsAdded[ # ] == PrimeFactorExponentsAdded[ # + 2] == 2 &]
Select[Range[700],PrimeOmega[#]==PrimeOmega[#+2]==2&] (* Harvey P. Dale, Aug 20 2011 *)
SequencePosition[Table[If[PrimeOmega[n]==2,1,0],{n,700}],{1,,1}] [[All,1]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale, May 29 2017 *)

PARI

is(n)=if(n%2==0, return(n==4)); bigomega(n)==2 && bigomega(n+2)==2 \\ Charles R Greathouse IV, Feb 21 2017

Python

from sympy import factorint
from itertools import count, islice
def agen(): # generator of terms
    yield 4
    nxt = 0
    for k in count(5, 2):
        prv, nxt = nxt, sum(factorint(k+2).values())
        if prv == nxt == 2: yield k
print(list(islice(agen(), 53))) # Michael S. Branicky, Nov 26 2022