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A053429 Numbers n such that Catalan(n)+1 is prime. 4
0, 1, 2, 5, 11, 25, 69, 86, 90, 95, 104, 145, 203, 215, 227, 291, 309, 322, 337, 407, 480, 792, 823, 919, 1001, 1159, 2226, 2743, 2822, 4250, 8077, 8109, 16024, 17422, 23941, 25212, 25379, 28753, 30510, 31748, 33613, 45622 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
Primality up to Catalan(4250)+1 proved by PrimeForm.
The next term, if it exists, is > 50000. - Vaclav Kotesovec, Apr 27 2021
LINKS
EXAMPLE
Catalan(25)+1 = 50!/25!/26!+1 = 4861946401453 is prime.
MATHEMATICA
Reap[ Do[ If[ PrimeQ[ CatalanNumber[n] + 1], Print[n]; Sow[n]], {n, 0, 10^4}]][[2, 1]] (* Jean-François Alcover, Feb 02 2015 *)
Select[Range[0, 29000], PrimeQ[CatalanNumber[#]+1]&] (* Harvey P. Dale, Apr 14 2019 *)
PROG
(PARI) is(n)=ispseudoprime(binomial(2*n, n)/(n+1)-1) \\ Charles R Greathouse IV, Jan 03 2014
(PFGW) ABC2 C(2*$a, $a)/($a+1)+1
a: from 0 to 100000
CROSSREFS
Sequence in context: A047775 A001432 A127075 * A266879 A104237 A085945
KEYWORD
nonn
AUTHOR
David Broadhurst, Jan 10 2000
EXTENSIONS
a(31)-a(38) from Charles R Greathouse IV, Jan 04 2014
a(39)-a(41) from Vaclav Kotesovec, Apr 20 2021
a(42) from Vaclav Kotesovec, Apr 26 2021
STATUS
approved

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Last modified March 29 11:45 EDT 2024. Contains 371278 sequences. (Running on oeis4.)