OFFSET
0,2
COMMENTS
The limit of b(n) is 5/2.
REFERENCES
Clifford A. Pickover, A Passion for Mathematics, Wiley, 2005.
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..284
EXAMPLE
b(1) = (2^2 + 1)/(2^2 - 1) = 5/3, so a(1) = 5.
b(2) = 5/3 * (3^2 + 1)/(3^2 - 1) = 25/12, so a(2) = 25.
b(3) = 25/12 * (5^2 + 1)/(5^2 - 1) = 325/144, so a(3) = 325.
b(4) = 325/144 * (7^2 + 1)/(7^2 - 1) = 8125/3456, so a(4) = 8125.
MATHEMATICA
a[n_]:= If[n==0, 1, Numerator[Product[(Prime[k]^2 + 1)/(Prime[k]^2 - 1), {k, n}]]]; Table[a[n], {n, 0, 15}] (* Indranil Ghosh, Apr 22 2017 *)
PROG
(PARI) a(n) = if (n==0, 1, numerator(prod(k=1, n, (prime(k)^2 + 1)/(prime(k)^2 - 1)))); \\ Michel Marcus, Apr 22 2017
CROSSREFS
KEYWORD
nonn,frac
AUTHOR
Seiichi Manyama, Apr 22 2017
STATUS
approved