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A070552
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Semiprimes k such that k+1 is also a semiprime.
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33
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9, 14, 21, 25, 33, 34, 38, 57, 85, 86, 93, 94, 118, 121, 122, 133, 141, 142, 145, 158, 177, 201, 202, 205, 213, 214, 217, 218, 253, 298, 301, 302, 326, 334, 361, 381, 393, 394, 445, 446, 453, 481, 501, 514, 526, 537, 542, 553, 565, 622, 633, 634, 694, 697
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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MATHEMATICA
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f[n_]:=Last/@FactorInteger[n]=={1, 1}||Last/@FactorInteger[n]=={2}; lst={}; Do[If[f[n]&&f[n+1], AppendTo[lst, n]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 25 2010 *)
Flatten[Position[Partition[Table[If[PrimeOmega[n]==2, 1, 0], {n, 700}], 2, 1], {1, 1}]] (* Harvey P. Dale, Feb 04 2015 *)
Select[Range[700], PrimeOmega[#] == PrimeOmega[# + 1] == 2 &] (* Vincenzo Librandi, Jan 22 2016 *)
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PROG
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(PARI) forprime(p=3, 1e3, if(bigomega(2*p-1)==2, print1(2*p-1", ")); if(bigomega(2*p+1)==2, print1(2*p", "))) \\ Charles R Greathouse IV, Nov 09 2011
(PARI) is(n)=if(n%2, isprime((n+1)/2) && bigomega(n)==2, isprime(n/2) && bigomega(n+1)==2) \\ Charles R Greathouse IV, Sep 08 2015
(Magma) IsSemiprime:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ n: n in [4..700] | IsSemiprime(n) and IsSemiprime(n+1) ]; // Vincenzo Librandi, Jan 22 2016
(Python)
from sympy import factorint
def is_semiprime(n): return sum(e for e in factorint(n).values()) == 2
def ok(n): return is_semiprime(n) and is_semiprime(n+1)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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Sharon Sela (sharonsela(AT)hotmail.com), May 03 2002
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EXTENSIONS
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STATUS
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approved
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