A285602 a(0) = 1; for n>1, a(n) is the numerator of b(n) = Product_{i=1..n} (prime(i)^2 + 1)/(prime(i)^2 - 1).

1, 5, 25, 325, 8125, 99125, 8425625, 1221715625, 44226105625, 11719917990625, 986817094810625, 94931804520782125, 65028286096735755625, 10937757721470954096125, 10117425892360632538915625, 11179755611058498955501765625

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

Cf. A000040, A285603.

Sequence in context: A145773 A197195 A358545 * A072324 A204544 A082026

Adjacent sequences: A285599 A285600 A285601 * A285603 A285604 A285605

Keyword

nonn,frac

Author

Seiichi Manyama, Apr 22 2017

Status

approved