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#14 by Charles R Greathouse IV at Wed Feb 01 01:10:04 EST 2017
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#13 by Charles R Greathouse IV at Wed Feb 01 01:08:52 EST 2017
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| COMMENTS
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Minimal "almost prime" triprimes (A014612) of the form prime(n) + prime(n+1).
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#12 by Charles R Greathouse IV at Wed Feb 01 01:07:30 EST 2017
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| PROG
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(PARI) list(lim)=my(v=List()); forprime(p=2, lim\2, forprime(q=2, min(p, lim\p\2), my(t=2*p*q); if(precprime(p*q)+nextprime(p*q)==t, listput(v, t)))); Set(v) \\ Charles R Greathouse IV, Feb 01 2017
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| STATUS
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proposed
editing
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#11 by Jon E. Schoenfield at Tue Jan 31 20:10:08 EST 2017
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#10 by Jon E. Schoenfield at Tue Jan 31 20:08:57 EST 2017
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| NAME
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Numbers that are the product of exactly 3-almost primes and are of the form prime(n) + prime(n+1).
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| COMMENTS
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Intersection of A001043 and A014612 ::
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| FORMULA
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a(n) is equal to 3-almost prime ifthe aproduct semiprimeof is3 equalprimes toif the arithmetic mean of prime(n) and prime(n+1).) is a semiprime.
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| EXAMPLE
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a(2)=) = 12 because 12= = 5+ + 7= = 3*2^2;
a(3)=) = 18 because 18= = 7+ + 11= = 2*3^2.
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| MATHEMATICA
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Select[Range[8, 10000, 2], 3 == PrimeOmega[#] && NextPrime[#/2] + NextPrime[#/2, -1] == # &] - _] == # &] (* _Zak Seidov_, Jan 31 2017 *)
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| CROSSREFS
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Cf. A014612, A001043, A014612.
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| STATUS
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proposed
editing
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Discussion
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| Tue Jan 31
| 20:10
| Jon E. Schoenfield: @Editors -- I did some rewording to try to avoid the use of the term "3-almost prime" ... but I'm not sure what to do with the phrase "almost prime" in the Comments.
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#9 by Zak Seidov at Tue Jan 31 06:22:13 EST 2017
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#8 by Zak Seidov at Tue Jan 31 06:21:46 EST 2017
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#7 by Zak Seidov at Tue Jan 31 06:20:48 EST 2017
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#6 by Zak Seidov at Tue Jan 31 06:16:04 EST 2017
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| LINKS
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Zak Seidov, <a href="/A105936/b105936.txt">Table of n, a(n) for n = 1..1000</a>
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| MATHEMATICA
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Select[Range[8, 10000, 2], 3 == PrimeOmega[#] && NextPrime[#/2] + NextPrime[#/2, -1] == # &] - Zak Seidov, Jan 31 2017
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| CROSSREFS
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Cf. A014612, A001043.
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| STATUS
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approved
editing
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#5 by Russ Cox at Fri Mar 30 18:50:49 EDT 2012
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| EXTENSIONS
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More terms from _Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), _, May 03 2005
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Discussion
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| Fri Mar 30
| 18:50
| OEIS Server: https://oeis.org/edit/global/246
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