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Engel expansion of zeta(3) = 1.20206... .
3

%I #35 Apr 13 2018 11:14:30

%S 1,5,98,127,923,5474,16490,25355,37910,85150,1033216,2290644,7844861,

%T 11170684,18884358,21481832,35060787,52399788,201059261,261533994,

%U 9939708446,211698940106,3030068839686,4326424644987,6082687570463

%N Engel expansion of zeta(3) = 1.20206... .

%C Cf. A006784 for definition of Engel expansion.

%D F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191.

%H G. C. Greubel, <a href="/A053980/b053980.txt">Table of n, a(n) for n = 1..1000</a>

%H F. Engel, <a href="/A006784/a006784.pdf">Entwicklung der Zahlen nach Stammbruechen</a>, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191. English translation by Georg Fischer, included with his permission.

%H P. Erdős and Jeffrey Shallit, <a href="http://www.numdam.org/item?id=JTNB_1991__3_1_43_0">New bounds on the length of finite Pierce and Engel series</a>, Sem. Theor. Nombres Bordeaux (2) 3 (1991), no. 1, 43-53.

%H <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>

%t 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 ] ]

%Y Cf. A006784, A028254, A028257.

%Y Cf. A002117, A067912.

%K nonn,easy,nice

%O 1,2

%A _Jeppe Stig Nielsen_, Apr 02 2000

%E More terms and additional comments from _Mitch Harris_, Jan 15 2001