A007541 Incrementally largest terms in the continued fraction for Pi-2 (cf. A001203).

1, 7, 15, 292, 436, 20776, 78629, 179136, 528210, 12996958, 878783625, 5408240597, 5916686112, 9448623833, 9787547328, 52662113289

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn

Comments

No larger term in the first 10,672,905,501 terms of the c.f. - Eric W. Weisstein, Jul 18 2013

References

• R. W. Gosper, Jr., Table of the simple continued fraction for pi and the derived decimal approximation, Math. Comp., 31 (1977), 1044.
• R. W. Gosper, personal communication.
• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
• See A001203 for many additional references and links.

Links

• H. Havermann, Simple Continued Fraction for Pi [a 483 MB file containing 180 million terms]
• Eric Weisstein's World of Mathematics, Pi
• Eric Weisstein's World of Mathematics, Pi Continued Fraction
• Index entries for sequences related to the number Pi

Crossrefs

Cf. A001203, A000796, A033090.

Apart from initial term, same as A033089.

Programs

Mathematica

upto=10^7;a={};r=0;f=ContinuedFraction[Pi-2,upto];Do[If[f[[i]]>r,AppendTo[a,r=f[[i]]]],{i, upto}];a (* Paolo Xausa, Nov 28 2021 *)

PARI

allocatemem(4096*10^6);
default(realprecision, 50000);
v = contfrac(Pi-2);
m = 0;
for (i=1, #v, if (v[i] > m, m = v[i]; print1(m, ", "))); \\ Michel Marcus, Aug 05 2017; to get 7 terms

Extensions

Corrected (missing a(9) added) by Eric W. Weisstein, Dec 08 2010

a(12) from Eric W. Weisstein, Dec 08 2010

a(13) from Eric W. Weisstein, Sep 16 2011

a(14) from Eric W. Weisstein, Sep 17 2011

a(15) from Eric W. Weisstein, Jul 18 2013

a(6) corrected by Bobby Jacobs, Aug 05 2017

a(16) = A033089(16) from Jeppe Stig Nielsen, Nov 28 2021