A285603 a(0) = 1; for n>1, a(n) is the denominator of b(n) = Product_{i=1..n} (prime(i)^2 + 1)/(prime(i)^2 - 1).

1, 3, 12, 144, 3456, 41472, 3483648, 501645312, 18059231232, 4767637045248, 400481511800832, 38446225132879872, 26297217990889832448, 4417932622469491851264, 4082169743161810470567936, 4506715396450638759507001344, 486725262816668986026756145152

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) = 3.
b(2) = 5/3 * (3^2 + 1)/(3^2 - 1) = 25/12, so a(2) = 12.
b(3) = 25/12 * (5^2 + 1)/(5^2 - 1) = 325/144, so a(3) = 144.
b(4) = 325/144 * (7^2 + 1)/(7^2 - 1) = 8125/3456, so a(4) = 3456.

Mathematica

a[n_]:= If[n==0, 1, Denominator[Product[(Prime[k]^2 + 1)/(Prime[k]^2 - 1), {k, n}]]]; Table[a[n], {n, 0, 16}] (* Indranil Ghosh, Apr 22 2017 *)

Prog

(PARI) a(n) = if (n==0, 1, denominator(prod(k=1, n, (prime(k)^2 + 1)/(prime(k)^2 - 1)))); \\ Michel Marcus, Apr 22 2017

Crossrefs

Cf. A000040, A285602.

Sequence in context: A363412 A322227 A254433 * A329471 A098152 A028301

Adjacent sequences: A285600 A285601 A285602 * A285604 A285605 A285606

Keyword

nonn,frac

Author

Seiichi Manyama, Apr 22 2017

Status

approved