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A092207
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Semiprimes k such that k+2 is also a semiprime.
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13
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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
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OFFSET
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1,1
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COMMENTS
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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
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LINKS
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Eric Weisstein's World of Mathematics, Semiprime
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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