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 A006525 Denominators of greedy Egyptian fraction for e - 2. (Formerly M1553) 29
 2, 5, 55, 9999, 3620211523, 25838201785967533906, 3408847366605453091140558218322023440765 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A greedy Egyptian fraction is also called a Sylvester expansion. - Robert FERREOL, May 02 2020 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 22 2020] H. P. Robinson, Letter to N. J. A. Sloane, Sep 1975 Eric Weisstein's World of Mathematics, Egyptian Fraction Wikipedia, Greedy algorithm for Egyptian fractions Index entries for sequences related to Egyptian fractions FORMULA a(n) = ceiling(1/(e - 2 - Sum_{j=0..n-1} 1/a(j))). - Jon E. Schoenfield, Dec 26 2014 EXAMPLE e - 2 = 1/2 + 1/5 + 1/55 + 1/9999 + ... . - Jon E. Schoenfield, Dec 26 2014 MATHEMATICA lst={}; k=N[E-2, 1000000]; 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 = exp(1) - 2; 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 Cf. A006526, A269993. Cf. A001466 (similar for Pi-3). Sequence in context: A114029 A013171 A073422 * A254406 A260654 A339167 Adjacent sequences: A006522 A006523 A006524 * A006526 A006527 A006528 KEYWORD nonn,frac AUTHOR N. J. A. Sloane EXTENSIONS More terms from Herman P. Robinson Offset changed to 1 by Indranil Ghosh, Mar 27 2017 STATUS approved

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Last modified August 8 12:42 EDT 2024. Contains 375021 sequences. (Running on oeis4.)