OFFSET
2,1
LINKS
Harvey P. Dale, Table of n, a(n) for n = 2..1000
EXAMPLE
c(n) - 1: 3, 5, 719, 11, 3359, 17, 9239.
c(n) + 1: 5, 7, 721, 13, 3361, 19, 9241. Here, for example, for we have twin primes except for n = 4, since 721 is not prime.
MATHEMATICA
z = 400; c[n_] := Product[k, {k, Prime[n] + 1, Prime[n + 1] - 1}]; d[n_] := If[PrimeQ[c[n] - 1], 1, 0]; t1 = Table[d[n], {n, 1, z}]; u1 = Flatten[Position[t1, 1]]; e[n_] := If[PrimeQ[c[n] + 1], 1, 0]; t2 = Table[e[n], {n, 1, z}]; u2 = Flatten[Position[t2, 1]]; u = Intersection[u1, u2]
pcnQ[n_]:=Module[{p=Times@@Range[Prime[n]+1, Prime[n+1]-1]}, AllTrue[p+{1, -1}, PrimeQ]]; Select[Range[250], pcnQ] (* Harvey P. Dale, Jan 28 2023 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Clark Kimberling, Oct 09 2013
STATUS
approved