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

3,2

Links

Table of n, a(n) for n=3..59.

Formula

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

Example

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

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!}]

Crossrefs

Cf. A000108, A078611.

Sequence in context: A122366 A228781 A103327 * A065229 A233037 A275999

Adjacent sequences: A177460 A177461 A177462 * A177464 A177465 A177466

Keyword

nonn

Author

Vladimir Joseph Stephan Orlovsky, May 09 2010

Status

approved