A091930 Write Pi = Sum_{n>=1} 1/sqrt(a(n)), where each a(n) is minimal and unique and the sum approaches Pi from below.

1, 2, 3, 4, 8, 77929, 17700337092966627, 97049570583433629023486339792437254323980677153951, 5843929411147236787850533935034401259024361461871518737494060444501523486808548249023180720047062910088805381472125716317734317997138497838459864230713

Offset

1,2

Comments

The first eight terms give Pi accurately to the first 75 decimal digits.

Links

Table of n, a(n) for n=1..9.

Formula

a(1) = 1, a(2) = 2, a(3) = 3, a(4) = 4; a(n) = ceiling((Pi - Sum_{i=1..n-1}(1/sqrt(a(i))))^-2).

Example

Pi > 1/sqrt(1) + 1/sqrt(2) + 1/sqrt(3) + 1/sqrt(4) + 1/sqrt(8), but Pi < 1/sqrt(1) + 1/sqrt(2) + 1/sqrt(3) + 1/sqrt(4) + 1/sqrt(7).

Mathematica

a[1] = 1; a[2] = 2; a[3] = 3; a[4] = 4; a[n_] := Ceiling[(Pi - Sum[1/Sqrt[a[i]], {i, 1, n - 1}])^-2]; Table[ a[n], {n, 1, 9}]

Crossrefs

Cf. A000796.

Sequence in context: A217353 A258194 A033554 * A124526 A124418 A175177

Adjacent sequences: A091927 A091928 A091929 * A091931 A091932 A091933

Keyword

nonn

Author

Robert G. Wilson v, Feb 13 2004

Status

approved