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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.
0
1, 1, 1, 3, 6, 20, 71, 431, 11111, 1096517, 3060614764, 139873870750394, 2228164248308209927663, 137936736998106949095632586591612, 1537967284879934603600637815040145351018766857006
OFFSET
1,4
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
KEYWORD
nonn
AUTHOR
Hauke Worpel (hw1(AT)email.com), Nov 11 2006
STATUS
approved