A123559 - OEIS

%I #11 Sep 06 2024 16:53:59

%S 1,1,1,3,6,20,71,431,11111,1096517,3060614764,139873870750394,

%T 2228164248308209927663,137936736998106949095632586591612,

%U 1537967284879934603600637815040145351018766857006

%N 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.

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

%e 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...

%o (PARI) f(x)=ceil(sqrt(1/x))

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

%K nonn

%O 1,4

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