A054543 - OEIS

A054543

Engel series expansion (or "Egyptian product") for Catalan's constant G.

2, 2, 2, 4, 4, 5, 5, 12, 13, 41, 110, 172, 248, 309, 3146, 5919, 21959, 22299, 30892, 401838, 1719239, 30576561, 262313756, 630913752, 3242181301, 3250783944, 13827502849, 40152067840, 137791590233, 2514510232695, 3217773878849

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,1

REFERENCES

S. R. Finch, Mathematical Constants, Cambridge, 2003, pp. 53-59.

LINKS

Simon Plouffe, Table of n, a(n) for n = 1..212

Steven R. Finch, Catalan's Constant [Broken link]

Steven R. Finch, Catalan's Constant [From the Wayback machine]

Oleg Marichev, Jonathan Sondow, and Eric W. Weisstein, Catalan's Constant, MathWorld.

Eric Weisstein's World of Mathematics, Engel Expansion

Index entries for sequences related to Engel expansions

MATHEMATICA

EngelExp[A_, n_]:=Join[Array[1&, Floor[A]], First@Transpose@NestList[{Ceiling[1/Expand[ #[[1]]#[[2]]-1]], Expand[ #[[1]]#[[2]]-1]}&, {Ceiling[1/(A-Floor[A])], A-Floor[A]}, n-1]]; EngelExp[N[Catalan, 7! ], 50] (* Vladimir Joseph Stephan Orlovsky, Jun 08 2009 *)

CROSSREFS

Cf. A006784, A028254, A028257, A006752, A104338, A014538, A153069, A153070, A118323.

Sequence in context: A096323 A282562 A035682 * A240861 A029046 A035372

Adjacent sequences: A054540 A054541 A054542 * A054544 A054545 A054546

KEYWORD

nonn

AUTHOR

Jeppe Stig Nielsen, Apr 09 2000

STATUS

approved