A123560 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 e.

1, 1, 2, 2, 3, 4, 5, 15, 67, 535, 8986, 912849, 1662587477, 81083409799344, 651628371908007046307, 17425286333232464262345491287814, 67473400772659322911375035883722405962101960016

Offset

1,3

Links

Table of n, a(n) for n=1..17.

Formula

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

Example

a(4) = 2 because the first three terms of the sequence are 1,1,2 and 2 is the smallest integer k such that 1/1^2 + 1/1^2 + 1/2^2 + 1/k^2 < e.

Prog

(PARI) l(x)=ceil(sqrt(1/x)); k=exp(1); for(T=1, 50, print(l(k)); k=k-1/l(k)^2)}

Crossrefs

Sequence in context: A210642 A263140 A205006 * A060407 A083702 A074077

Adjacent sequences: A123557 A123558 A123559 * A123561 A123562 A123563

Keyword

nonn

Author

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

Status

approved