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A134776
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Primes that are the sum of first k Catalan numbers for some integer k.
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1
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OFFSET
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1,1
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COMMENTS
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Next term a(7) has 475 decimal digits and is too large to include. Corresponding numbers k such that the sum of first k Catalan numbers is a prime are listed in A134775.
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LINKS
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FORMULA
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EXAMPLE
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a(1) = 3 because C(1) + C(2) = 1 + 2 = 3 is a prime.
a(2) = 6917 because C(1) + C(2) + C(3) + C(4) + C(5) + C(6) + C(7) + C(8) + C(9) = 1 + 2 + 5 + 14 + 42 + 132 + 429 + 1430 + 4862 = 6917 is a prime.
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MATHEMATICA
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f=0; Do[ f = f + Binomial[ 2n, n ]/(n+1); If[ PrimeQ[f], Print[ {n, f} ] ], {n, 1, 1000} ]
Select[Accumulate[CatalanNumber[Range[200]]], PrimeQ] (* Harvey P. Dale, Mar 01 2019 *)
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CROSSREFS
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Cf. A134475 (numbers k such that the sum of first k Catalan numbers is a prime).
Cf. A014138 (partial sums of Catalan numbers).
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KEYWORD
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hard,nonn
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AUTHOR
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STATUS
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approved
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