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A234095
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Primes p such that 2*p + 1 is semiprime.
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11
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7, 17, 19, 43, 47, 59, 61, 71, 79, 101, 107, 109, 149, 151, 163, 167, 197, 223, 257, 263, 271, 311, 317, 347, 349, 353, 383, 389, 401, 421, 439, 449, 461, 479, 503, 521, 523, 557, 569, 599, 601, 613, 631, 673, 677, 691, 701, 811, 821, 827, 839, 853, 863, 881
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OFFSET
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1,1
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COMMENTS
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Also primes of the form (p*q - 1)/2, where p and q are distinct primes.
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LINKS
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FORMULA
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EXAMPLE
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7 is in the sequence because it is prime and 7*2 + 1 = 15 = 3*5 is a semiprime.
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MATHEMATICA
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t = Select[Range[1, 7000, 2], Map[Last, FactorInteger[#]] == Table[1, {2}] &]; Take[(t - 1)/2, 120] (* A234093 *)
v = Flatten[Position[PrimeQ[(t - 1)/2], True]] ; w = Table[t[[v[[n]]]], {n, 1, Length[v]}] (* A233561 *)
Select[Prime[Range[200]], PrimeOmega[2#+1]==2&] (* Harvey P. Dale, Mar 19 2015 *)
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PROG
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(Magma) IsSemiprime:=func< p | &+[ k[2]: k in Factorization(p)] eq 2 >; [p: p in PrimesUpTo(1000)| IsSemiprime(2*p+1)]; // Vincenzo Librandi, Feb 21 2014
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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