A264042 Prime numbers adjacent to Catalan numbers (A000108).

2, 3, 13, 41, 43, 131, 1429, 4861, 58787, 477638699, 4861946401451, 4861946401453, 5632681584560312734993915705849145099, 337485502510215975556783793455058624701, 4180080073556524734514695828170907458428751314321, 16435314834665426797069144960762886143367590394939

Offset: 1

Author

Bill McEachen, Nov 01 2015

Keywords

• nonn

Comments

A230061 and A231885 are a subset of this sequence.

The following are twin primes off of the n-th Catalan number: 5, 25, 145, ..., (11500). - Robert G. Wilson v, Nov 10 2015

Examples

			A000108(5)=42 and both 41 and 43 are adjacent prime numbers, and thus are sequence members.
		

Links

• Bill McEachen, Table of n, a(n) for n = 1..52

Crossrefs

Cf. A000108 (Catalan numbers).

Cf. A173868 (smallest primes > Catalan numbers).

Cf. A231885, A230061 (Catalan(n)-1 and Catalan(n)+1 that are primes).

Programs

Mathematica

Select[Union[# - 1, # + 1] &@ Table[(2 n)!/n!/(n + 1)!, {n, 100}], PrimeQ] (* Michael De Vlieger, Nov 05 2015 *)

PARI

A264042()={for (n=1,10000,if(n<3,q=binomial(2*n,n)/(n+1)); if(n>2,q=2*qold1*(8*qold2+qold1)/(10*qold2-qold1)); qold2=qold1; qold1=q; if(ispseudoprime(q-1),print1(q-1,"," )); if(ispseudoprime(q+1),print1(q+1,"," )));}

PARI

C=1; for(n=1,1e3, C*=2*(2*n-1)/(n+1); if(ispseudoprime(C-1), print1(C-1", ")); if(ispseudoprime(C+1), print1(C+1", "))) \\ Charles R Greathouse IV, Nov 05 2015