This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A264042 #33 Jun 02 2025 12:15:29
%S A264042 2,3,13,41,43,131,1429,4861,58787,477638699,4861946401451,
%T A264042 4861946401453,5632681584560312734993915705849145099,
%U A264042 337485502510215975556783793455058624701,4180080073556524734514695828170907458428751314321,16435314834665426797069144960762886143367590394939
%N A264042 Prime numbers adjacent to Catalan numbers (A000108).
%C A264042 A230061 and A231885 are a subset of this sequence.
%C A264042 The following are twin primes off of the n-th Catalan number: 5, 25, 145, ..., (11500). - _Robert G. Wilson v_, Nov 10 2015
%H A264042 Bill McEachen, <a href="/A264042/b264042.txt">Table of n, a(n) for n = 1..52</a>
%e A264042 A000108(5)=42 and both 41 and 43 are adjacent prime numbers, and thus are sequence members.
%t A264042 Select[Union[# - 1, # + 1] &@ Table[(2 n)!/n!/(n + 1)!, {n, 100}], PrimeQ] (* _Michael De Vlieger_, Nov 05 2015 *)
%o A264042 (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,"," )));}
%o A264042 (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
%Y A264042 Cf. A000108 (Catalan numbers).
%Y A264042 Cf. A173868 (smallest primes > Catalan numbers).
%Y A264042 Cf. A231885, A230061 (Catalan(n)-1 and Catalan(n)+1 that are primes).
%K A264042 nonn
%O A264042 1,1
%A A264042 _Bill McEachen_, Nov 01 2015