A058286 Continued fraction for Pi^4.

97, 2, 2, 3, 1, 16539, 1, 6, 7, 6, 8, 6, 3, 9, 1, 1, 1, 18, 1, 4, 1, 13, 1, 2, 1, 127, 1, 1, 1, 4, 1, 6, 1, 1, 1, 10, 10, 1, 1, 2, 1, 2, 1, 5, 1, 1, 10, 1, 3, 2, 1, 1, 4, 9, 1, 7, 70, 1, 13, 1, 2, 6, 1, 2, 24, 5, 2, 6, 1, 1, 1, 8, 1, 1, 11, 2, 1, 1, 4, 3, 1, 3, 2, 2, 1, 7, 1, 4, 1, 22, 2, 1, 2, 3, 1

Offset

0,1

Comments

"Truncating just before the unexpectedly large partial quotient 16,539 gives a famous approximation of Ramanujan for Pi^4 of 97 9/22." (Wells)

References

David Wells, "The Penguin Dictionary of Curious and Interesting Numbers," Revised Edition, Penguin Books, London, England, 1997, page 116.

Links

Harry J. Smith, Table of n, a(n) for n = 0..20000

Example

97.4090910340024372364403326... = 97 + 1/(2 + 1/(2 + 1/(3 + 1/(1 + ...)))). - Harry J. Smith, Jun 22 2009

Mathematica

ContinuedFraction[ Pi^4, 100]

Prog

(PARI) { allocatemem(932245000); default(realprecision, 21000); x=contfrac(Pi^4); for (n=0, 20000, write("b058286.txt", n, " ", x[n+1])); } \\ Harry J. Smith, Jun 22 2009

Crossrefs

Cf. A092425 Decimal expansion. - Harry J. Smith, Jun 22 2009

Sequence in context: A249922 A163494 A117846 * A051330 A106429 A126840

Adjacent sequences: A058283 A058284 A058285 * A058287 A058288 A058289

Keyword

cofr,nonn,easy

Author

Robert G. Wilson v, Dec 07 2000

Status

approved