A067912 Engel expansion of zeta(4) = Pi^4/90 = Sum_{i>0} 1/i^4.

1, 13, 15, 19, 132, 1474, 1977, 10392, 12992, 44777, 59412, 170685, 217607, 704791, 818133, 1387423, 2208674, 3206215, 12732462, 13962681, 24593168, 39744274, 55804517, 130269696, 426536424, 546807194, 1030799587, 1139987135

Offset: 1

Author

Benoit Cloitre, Mar 03 2002

Keywords

• easy
• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 1..1000

Crossrefs

See A006784 for explanation of Engel expansions.

Cf. A059186, A053980.

Programs

Mathematica

EngelExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@
NestList[{Ceiling[1/Expand[#[[1]] #[[2]] - 1]], Expand[#[[1]] #[[2]] - 1]/1} &, {Ceiling[1/(A - Floor[A])], (A - Floor[A])/1}, n - 1]]; EngelExp[N[Pi^4/90, 7!], 20] (* G. C. Greubel, Dec 26 2016 *)