A092207 - OEIS

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

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

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 *)

PROG

(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