A177463 The smallest k such that Catalan(n)+k and Catalan(n)-k are both prime.

0, 3, 1, 5, 10, 3, 69, 33, 45, 45, 9, 47, 86, 97, 97, 41, 19, 49, 191, 11, 101, 283, 1, 69, 597, 549, 1341, 243, 552, 121, 157, 115, 1341, 1905, 165, 597, 27, 87, 31, 731, 1093, 449, 127, 37, 37, 157, 1145, 587, 317, 659, 1523, 487, 865, 4879, 463, 1351, 4471

Offset: 3

Author

Vladimir Joseph Stephan Orlovsky, May 09 2010

Keywords

• nonn

Examples

			5 +- 0 -> primes, 14 +- 3 -> primes, 42 +- 1 -> primes, 132 +- 5 -> primes, ...
		

Crossrefs

Cf. A000108, A078611.

Programs

Maple

A000108 := proc(n) binomial(2*n,n)/(n+1) ; end proc:
A047160 := proc(n) for k from 0 to n-1 do if isprime(n-k) and isprime(n+k) then return k; end if; end do: return -1 ; end proc:
A177463 := proc(n) A047160(A000108(n)) ; end proc:
seq(A177463(n),n=3..40) ; # R. J. Mathar, Jan 23 2011

Mathematica

g[n_]:=(2n)!/n!/(n+1)!; f[n_]:=Block[{k},If[OddQ[n],k=0,k=1];While[ !PrimeQ[n-k]||!PrimeQ[n+k],k+=2];k]; Table[f[g[n]],{n,3,4*4!}]

Formula

a(n) = A047160(A000108(n)). - R. J. Mathar, Jan 23 2011