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

Author

Robert G. Wilson v, Dec 07 2000

Keywords

• cofr
• nonn
• easy

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)

Examples

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

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

Crossrefs

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

Programs

Mathematica

ContinuedFraction[ Pi^4, 100]

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