

A007541


Incrementally largest terms in the continued fraction for Pi2 (cf. A001203).
(Formerly M4351)


3



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

Table of n, a(n) for n=1..15.
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


PROG

(PARI) allocatemem(4096*10^6);
default(realprecision, 50000);
v = contfrac(Pi2);
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

Cf. A001203, A000796, A033090.
Apart from initial term, same as A033089.
Sequence in context: A042725 A041096 A248275 * A087485 A156377 A069526
Adjacent sequences: A007538 A007539 A007540 * A007542 A007543 A007544


KEYWORD

nonn


AUTHOR

N. J. A. Sloane


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


STATUS

approved



