|
|
A121852
|
|
Numbers n such that partial sum of Catalan numbers A014137(n) is a prime.
|
|
2
|
|
|
1, 4, 6, 16, 24, 104, 121, 283, 326, 489, 1387, 1394, 1424, 1435, 1985, 4323, 5221
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,2
|
|
COMMENTS
|
Corresponding primes are A014137( a(n)) = {2,23,197,48760367,1757900019101,...}.
|
|
LINKS
|
|
|
EXAMPLE
|
Catalan numbers A000108(n) begin {1,1,2,5,14,42,132,429,1430,4862,...}.
a(1) = 1 because A014137(1) = 1 + 1 = 2 is prime,
a(2) = 4 because A014137(4) = 1 + 1 + 2 + 5 + 14 = 23 is prime.
|
|
MATHEMATICA
|
s = 1; Do[s = s + (2n)!/((n!)^2(n + 1)); If[PrimeQ@s, Print@n], {n, 17925}] (* Robert G. Wilson v *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
hard,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|