A006524 Egyptian fraction for 1/ Pi.

4, 15, 609, 845029, 1010073215739, 1300459886313272270974271, 1939680952094609786557359582286462958434022504402

Offset: 1

Author

N. J. A. Sloane, Robert G. Wilson v

Keywords

• nonn
• frac

References

• N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..11 [a(11) corrected by _Georg Fischer_, Jun 04 2019]
• H. P. Robinson, Letter to N. J. A. Sloane, Sep 1975
• Eric Weisstein's World of Mathematics, Egyptian Fraction
• Index entries for sequences related to the number Pi
• Index entries for sequences related to Egyptian fractions

Programs

Mathematica

a = {}; k = N[1/Pi, 1000]; Do[s = Ceiling[1/k]; AppendTo[a, s]; k = k - 1/s, {n, 1, 10}]; a (* Artur Jasinski, Sep 22 2008 *)

PARI

x = 1/Pi;
f(x, k) = if(k<1, x, f(x, k - 1) - 1/n(x, k));
n(x, k) = ceil(1/f(x, k - 1));
for(k = 1, 7, print1(n(x, k),", ")) \\ Indranil Ghosh, Mar 27 2017

Extensions

More terms from Herman P. Robinson

Offset changed to 1 by Indranil Ghosh, Mar 27 2017