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A065017
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p*q + p + q is prime, where (p, q=p+2) are twin primes.
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1
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23, 47, 167, 359, 1847, 3719, 10607, 19319, 97967, 177239, 273527, 657719, 1042439, 1104599, 1329407, 1515359, 1745039, 2042039, 4464767, 5013119, 5148359, 9740639, 11095559, 11377127, 12538679, 16024007, 16410599, 16752647
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| The resulting prime can never be a twin prime since the odd number preceding it is divisible by three and the following odd number is a perfect square.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1,...,1000
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FORMULA
| p^2+4*p+2.
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EXAMPLE
| (3*5) + (3+5) = 23
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MATHEMATICA
| NextPrim[n_] := Block[ {k = n + 1}, While[ !PrimeQ[k], k++ ]; Return[k]]; k = 1; Do[k = NextPrim[k]; If[ PrimeQ[k + 2], p = k*(k + 2) + 2k + 2; If[ PrimeQ[p], Print[p]]], {n, 1, 700} ]
f[n_]:=Module[{x=Total[n]+Times@@n}, If[PrimeQ[x], x, 0]]; Select[f/@ (Select[Partition[Prime[Range[700]], 2, 1], Last[#]-First[#]==2&]), #!=0&] (* From Harvey P. Dale, May 11 2011 *)
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PROG
| (PARI) { n=p=0; for (m=1, 10^9, p=nextprime(p + 1); if (isprime(q=p + 2) && isprime(a=p*q + p + q), write("b065017.txt", n++, " ", a); if (n==1000, return)) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 03 2009]
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CROSSREFS
| A049001, A049002
Sequence in context: A042050 A139857 A139900 * A140618 A042052 A136030
Adjacent sequences: A065014 A065015 A065016 * A065018 A065019 A065020
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KEYWORD
| nonn
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AUTHOR
| Stephan Wagler (stephanwagler(AT)aol.com), Nov 01 2001
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EXTENSIONS
| OFFSET changed from 0,1 to 1,1 by Harry J. Smith (hjsmithh(AT)sbcglobal.net), Oct 03 2009
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