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

Offset: 1

Author

Jeppe Stig Nielsen, Apr 09 2000

Keywords

• nonn

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

Crossrefs

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

Programs

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 *)