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A177463 The smallest k such that Catalan(n)+k and Catalan(n)-k are both prime. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 20 17:04 EST 2020. Contains 332080 sequences. (Running on oeis4.)