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Search: id:A134776
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| A134776 |
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Primes that are the sum of first n Catalan numbers. . |
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+0
2
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| 3, 6917, 82499, 19720133460129649, 11784299926611415613401489, 33787453028775764987481051710452890017437115179924200888710613777623666010771906\ 68071
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OFFSET
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1,1
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COMMENT
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Next term a(7) has 475 decimal digits and is too large to include. Corresponding numbers n such that the sum of first n Catalan numbers is a prime are listed in A134775(n) = {2, 9, 11, 31, 46, 146, 795, ...}.
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LINKS
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Eric Weisstein, Link to a section of The World of Mathematics. Catalan Number.
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FORMULA
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a(n) = A014138( A134775(n) - 1 ).
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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} ]
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CROSSREFS
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Cf. A134475 = Numbers n such that the sum of first n Catalan numbers is a prime. Cf. A014138 = Partial sums of Catalan numbers (starting 1, 2, 5, ..., cf. A000108). Cf. A000108 = Catalan numbers. .
Sequence in context: A003166 A034317 A056749 this_sequence A062595 A128147 A068918
Adjacent sequences: A134773 A134774 A134775 this_sequence A134777 A134778 A134779
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KEYWORD
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hard,nonn
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AUTHOR
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Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 11 2007
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