Search: id:A134776
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%I A134776
%S A134776 3,6917,82499,19720133460129649,11784299926611415613401489,
%T A134776 3378745302877576498748105171045289001743711517992420088871061377762366601077190668071
%N A134776 Primes that are the sum of first n Catalan numbers. .
%C A134776 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, ...}.
%H A134776 Eric Weisstein, Link to a section of The World of Mathematics. <a href="http:/
               /mathworld.wolfram.com/CatalanNumber.html">Catalan Number</a>.
%F A134776 a(n) = A014138( A134775(n) - 1 ).
%e A134776 a(1) = 3 because C(1) + C(2) = 1 + 2 = 3 is a prime.
%e A134776 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.
%t A134776 f=0; Do[ f = f + Binomial[ 2n, n ]/(n+1); If[ PrimeQ[f], Print[ {n, f} 
               ] ], {n, 1, 1000} ]
%Y A134776 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. .
%Y A134776 Sequence in context: A003166 A034317 A056749 this_sequence A062595 A128147 
               A068918
%Y A134776 Adjacent sequences: A134773 A134774 A134775 this_sequence A134777 A134778 
               A134779
%K A134776 hard,nonn
%O A134776 1,1
%A A134776 Alexander Adamchuk (alex(AT)kolmogorov.com), Nov 11 2007

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