A001466 Denominators of greedy Egyptian fraction expansion of Pi - 3. (Formerly M4553 N1935)

8, 61, 5020, 128541455, 162924332716605980, 28783052231699298507846309644849796, 871295615653899563300996782209332544845605756266650946342214549769447

Offset

1,1

Comments

A greedy Egyptian fraction expansion is also called a Sylvester expansion. - Robert FERREOL, May 02 2020

References

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

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

Links

Simon Plouffe, Table of n, a(n) for n = 1..10 (There is a limit of about 1000 digits on the size of numbers in b-files)

Mohammad K. Azarian, An Expression for Pi, Problem #870, College Mathematics Journal, Vol. 39, No. 1, January 2008, p. 66. Solution appeared in Vol. 40, No. 1, January 2009, pp. 62-64.

K. R. R. Gandhi, Edifice of the real numbers by alternating series, International Journal of Mathematical Archive-3(9), 2012, 3277-3280. - From N. J. A. Sloane, Jan 02 2013

Simon Plouffe, Table of n, a(n) for n = 1..14

H. P. Robinson, Letter to N. J. A. Sloane, Sep 1975

H. E. Salzer, The approximation of numbers as sums of reciprocals, Amer. Math. Monthly, 54 (1947), 135-142.

Eric Weisstein's World of Mathematics, Egyptian Fraction

Wikipedia, Greedy algorithm for Egyptian fractions

J. W. Wrench, Jr., Letter to N. J. A. Sloane, Mar 27 1974

Index entries for sequences related to the number Pi

Example

Pi - 3 = 1/8 + 1/61 + 1/5020 + 1/128541455 + ... .

Mathematica

lst={}; k=N[(Pi-3), 1000]; Do[s=Ceiling[1/k]; AppendTo[lst, s]; k=k-1/s, {n, 12}]; lst (* Vladimir Joseph Stephan Orlovsky, Nov 02 2009 *)

Prog

(PARI) x = Pi - 3;
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

Crossrefs

See A182257, A224230 for other versions of this sequence.

Cf. A006525 (similar for e-2).

Sequence in context: A327761 A080525 A362944 * A182257 A082179 A114028

Adjacent sequences: A001463 A001464 A001465 * A001467 A001468 A001469

Keyword

nonn,frac

Author

N. J. A. Sloane

Status

approved