The On-Line Encyclopedia of Integer Sequences (OEIS)

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A121852

Numbers n such that partial sum of Catalan numbers A014137(n) is a prime.
(history; published version)

#6 by Jon E. Schoenfield at Fri Mar 20 18:26:56 EDT 2015

STATUS

editing

approved

#5 by Jon E. Schoenfield at Fri Mar 20 18:26:54 EDT 2015

EXTENSIONS

a(11) - a(17) from _Robert G. Wilson v, _, Aug 31 2006

STATUS

approved

editing

#4 by N. J. A. Sloane at Thu Oct 31 12:17:40 EDT 2013

MATHEMATICA

s = 1; Do[s = s + (2n)!/((n!)^2(n + 1)); If[PrimeQ@s, Print@n], {n, 17925}] (* _Robert G. Wilson v _ *)

Discussion

Thu Oct 31

12:17

OEIS Server: https://oeis.org/edit/global/2036

#3 by Russ Cox at Sat Mar 31 13:20:28 EDT 2012

AUTHOR

_Alexander Adamchuk (alex(AT)kolmogorov.com), _, Aug 30 2006

Discussion

Sat Mar 31

13:20

OEIS Server: https://oeis.org/edit/global/879

#2 by N. J. A. Sloane at Mon Oct 09 03:00:00 EDT 2006

MATHEMATICA

s = 1; Do[s = s + (2n)!/((n!)^2(n + 1)); If[PrimeQ@s, Print@n], {n, 17925}] (* RGWv Robert G. Wilson v *)

KEYWORD

hard,nonn,new

EXTENSIONS

a(11) - a(17) from RGWv, Robert G. Wilson v, Aug 31 2006

#1 by N. J. A. Sloane at Fri Sep 29 03:00:00 EDT 2006

NAME

Numbers n such that partial sum of Catalan numbers A014137(n) is a prime.

DATA

1, 4, 6, 16, 24, 104, 121, 283, 326, 489, 1387, 1394, 1424, 1435, 1985, 4323, 5221

OFFSET

1,2

COMMENTS

Corresponding primes are A014137( a(n)) = {2,23,197,48760367,1757900019101,...}.

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}] (* RGWv *)

CROSSREFS

Cf. A000108, A014137.

KEYWORD

hard,nonn,new

AUTHOR

Alexander Adamchuk (alex(AT)kolmogorov.com), Aug 30 2006

EXTENSIONS

a(11) - a(17) from RGWv, Aug 31 2006

STATUS

approved