A123559 a(n) is the smallest integer such that 1/a(1)^2 + 1/a(2)^2 + ... + 1/a(n-1)^2 + 1/a(n)^2 is less than Pi.

1, 1, 1, 3, 6, 20, 71, 431, 11111, 1096517, 3060614764, 139873870750394, 2228164248308209927663, 137936736998106949095632586591612, 1537967284879934603600637815040145351018766857006

Offset

1,4

Links

Table of n, a(n) for n=1..15.

Formula

a(n) = ceiling(sqrt(Pi - Sum_{i=1..n-1} 1/a(i)^2)).

Example

a(4)=3 because Pi - 1/a(1)^2 - 1/a(2)^2 - 1/a(3)^2 = Pi - 1 - 1 - 1 = 0.1415926... and 3 is the smallest integer such that 1/3^2 = 0.1111111... < 0.1415926...

Prog

(PARI) f(x)=ceil(sqrt(1/x))
lista(n)={my(k=Pi, v=vector(n)); for(T=1, n, v[T]= f(k); k-=1/v[T]^2); v}

Crossrefs

Sequence in context: A090371 A288817 A168594 * A334329 A162171 A194992

Adjacent sequences: A123556 A123557 A123558 * A123560 A123561 A123562

Keyword

nonn

Author

Hauke Worpel (hw1(AT)email.com), Nov 11 2006

Status

approved