|
|
A007541
|
|
Incrementally largest terms in the continued fraction for Pi-2 (cf. A001203).
(Formerly M4351)
|
|
3
|
|
|
1, 7, 15, 292, 436, 20776, 78629, 179136, 528210, 12996958, 878783625, 5408240597, 5916686112, 9448623833, 9787547328, 52662113289
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
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
|
Eric Weisstein's World of Mathematics, Pi
|
|
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.
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|