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A075840
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Primes of the form (2*n)!/(n!)^2+1.
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2
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2, 3, 7, 71, 3433, 2704157, 35345263801, 2104098963721, 6892620648693261354601, 410795449442059149332177041, 1520803477811874490019821888415218657, 5949105755928259715106809205795376486501, 1480212998448786189993816895482588794876101
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OFFSET
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1,1
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REFERENCES
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New Zealand Science Monthly, Bulletin Board, Feb. 1999. Binomial(300,150)+185 = nextprime.
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LINKS
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Charles R Greathouse IV, Table of n, a(n) for n = 1..25
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EXAMPLE
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7 is a term because C(4,2)+1 = 6+1 = 7 is prime.
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MATHEMATICA
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a = Select[ Range[100], PrimeQ[Binomial[2#, # ] + 1] & ]; Binomial[2a, a] + 1
Select[Table[(2 n)! / (n!)^2 + 1, {n, 0, 80}], PrimeQ] (* Vincenzo Librandi, Mar 17 2015 *)
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PROG
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(PARI) v=[]; for(n=0, 100, x=bin(2*n, n)+1; if(isprime(x), v=concat(v, x), )); v
(MAGMA) [a: n in [0..100] | IsPrime(a) where a is Factorial(2*n) div Factorial(n)^2+1]; // Vincenzo Librandi Mar 17 2015
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CROSSREFS
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Cf. A092751 = n such that (2*n)!/(n!)^2+1 is prime, A112858 = primes of the form (2*n)!/(n!)^2-1.
Cf. A000984, n's are in A066699.
Sequence in context: A130309 A090870 A088542 * A096225 A035094 A084729
Adjacent sequences: A075837 A075838 A075839 * A075841 A075842 A075843
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KEYWORD
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nonn
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AUTHOR
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Donald S. McDonald, Oct 14 2002
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EXTENSIONS
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Edited by Robert G. Wilson v, Oct 15 2002
Definition corrected by Alexander Adamchuk, Nov 30 2007
Edited by N. J. A. Sloane, Nov 30 2007
a(13) from Vincenzo Librandi, Mar 17 2015
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STATUS
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approved
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