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A230061
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Primes of the form Catalan(n)+1.
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4
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2, 3, 43, 58787, 4861946401453, 337485502510215975556783793455058624701, 4180080073556524734514695828170907458428751314321, 1000134600800354781929399250536541864362461089950801, 944973797977428207852605870454939596837230758234904051
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OFFSET
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1,1
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COMMENTS
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The 25th term a(25) in the sequence has 693 digits.
a(26) has 1335 digits; a(27) has 1647 digits; a(28) has 1694 digits; a(29) has 2554 digits; a(30) has 4857 digits; a(31) has 4876 digits; a(32) has 9641 digits. - Charles R Greathouse IV, Oct 09 2013
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LINKS
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EXAMPLE
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a(3)= 43: Catalan(5)= (2*5)!/(5!*(5+1)!)= 42. Catalan(5)+1= 43 which is prime.
a(4)= 58787: Catalan(11)= (2*11)!/(11!*(11+1)!)= 58786. Catalan(11)+1= 58787 which is prime.
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MAPLE
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KD:= proc() local a, b, c; a:= (2*n)!/(n!*(n + 1)!); b:=a+1; if isprime(b) then return(b): fi; end: seq(KD(), n=1..50);
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MATHEMATICA
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Select[CatalanNumber[Range[100]]+1, PrimeQ] (* Harvey P. Dale, Aug 26 2021 *)
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PROG
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(PARI) for(n=1, 1e3, if(ispseudoprime(t=binomial(2*n, n)/(n+1)+1), print1(t", "))) \\ Charles R Greathouse IV, Oct 08 2013
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CROSSREFS
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Cf. A053429 (numbers n such that Catalan(n)+1 is prime).
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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