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A140777
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a(n) = 2p(n) - 4, where p(n) is the n-th prime.
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2
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0, 2, 6, 10, 18, 22, 30, 34, 42, 54, 58, 70, 78, 82, 90, 102, 114, 118, 130, 138, 142, 154, 162, 174, 190, 198, 202, 210, 214, 222, 250, 258, 270, 274, 294, 298, 310, 322, 330, 342, 354, 358, 378, 382, 390, 394, 418, 442, 450, 454, 462, 474, 478, 498, 510, 522
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| A number n is included if (p + n/p) is prime, where p is the smallest prime that divides n. Since all terms of this sequence are even (or otherwise p + n/p would be even and not a prime), then p is always 2. So this sequence is the set of all even numbers n where (2 + n/2) is prime.
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EXAMPLE
| The smallest prime dividing 42 is 2. Since 2 + 42/2 = 23 is prime, then 42 is included in this sequence.
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MAPLE
| A020639 := proc(n) local dvs, p ; dvs := sort(convert(numtheory[divisors](n), list)) ; for p in dvs do if isprime(p) then RETURN(p) ; fi ; od: error("%d", n) ; end: A111234 := proc(n) local p ; p := A020639(n) ; p+n/p ; end: isA140777 := proc(n) RETURN(isprime(A111234(n))) ; end: for n from 2 to 1200 do if isA140777(n) then printf("%d, ", n) ; fi ; od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), May 31 2008
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MATHEMATICA
| fQ[n_] := Block[{p = First@ First@ Transpose@ FactorInteger@ n}, PrimeQ[p + n/p] == True]; Select[ Range[2, 533], fQ@# &] - Robert G. Wilson v, (rgwv(AT)rgwv.com), May 30 2008
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CROSSREFS
| Cf. A020639, A111234, A140775, A140776.
Sequence in context: A099540 A190695 A180739 * A050844 A077626 A174316
Adjacent sequences: A140774 A140775 A140776 * A140778 A140779 A140780
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KEYWORD
| nonn
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AUTHOR
| Leroy Quet May 29 2008, May 31 2008
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EXTENSIONS
| More terms from Robert G. Wilson v and R. J. Mathar (mathar(AT)strw.leidenuniv.nl), (rgwv(AT)rgwv.com), May 30 2008
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