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A134776
Primes that are the sum of first k Catalan numbers for some integer k.
1
3, 6917, 82499, 19720133460129649, 11784299926611415613401489, 3378745302877576498748105171045289001743711517992420088871061377762366601077190668071
OFFSET
1,1
COMMENTS
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.
LINKS
Eric Weisstein's World of Mathematics, Catalan Number
FORMULA
a(n) = A014138( A134775(n) - 1 ).
EXAMPLE
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.
MATHEMATICA
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 *)
CROSSREFS
Cf. A134775 (numbers k such that the sum of first k Catalan numbers is a prime).
Cf. A014138 (partial sums of Catalan numbers).
Cf. A000108 (Catalan numbers).
Sequence in context: A283019 A056749 A281788 * A062595 A128147 A326391
KEYWORD
hard,nonn
AUTHOR
Alexander Adamchuk, Nov 11 2007
STATUS
approved