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A007541
Incrementally largest terms in the continued fraction for Pi-2 (cf. A001203).
(Formerly M4351)
2
1, 7, 15, 292, 436, 20776, 78629, 179136, 528210, 12996958, 878783625, 5408240597, 5916686112, 9448623833, 9787547328, 52662113289
OFFSET
1,2
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
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 *)
PROG
(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
CROSSREFS
Apart from initial term, same as A033089.
Sequence in context: A042725 A041096 A248275 * A087485 A156377 A069526
KEYWORD
nonn
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
STATUS
approved