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A053427

Numbers n such that Catalan(n)-1 is prime.

4, 5, 6, 8, 9, 18, 25, 66, 87, 134, 145, 200, 384, 443, 502, 589, 625, 638, 1082, 1235, 1236, 1439, 1892, 2014, 2355, 2380, 2592, 2676, 2981, 3406, 3908, 4775, 5885, 10617, 16108, 17035, 18164, 18307, 20565, 24542, 26388, 32786, 47379, 49711, 50103, 55067

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

COMMENTS

Primality up to Catalan(5885)-1 proved by PrimeForm.

The next term, if it exists, is > 60000. - Vaclav Kotesovec, Apr 26 2021

LINKS

Table of n, a(n) for n=1..46.

EXAMPLE

Catalan(25)-1 = 50!/25!/26!-1 = 4861946401451 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 *)