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

1,1

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

Links

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A000108 (Catalan numbers).

Cf. A173868 (smallest primes > Catalan numbers).

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

Sequence in context: A141511 A235615 A117528 * A122719 A106866 A278139

Adjacent sequences: A264039 A264040 A264041 * A264043 A264044 A264045

Keyword

nonn

Author

Bill McEachen, Nov 01 2015

Status

approved