This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A053977 #33 Feb 16 2025 08:32:42
%S A053977 2,7,13,19,85,2601,9602,46268,4812284,147961485,210810243,814960948,
%T A053977 1003849128,1016803038,12917183059,26242325020,22215291139324,
%U A053977 30797877759859,60139200644343,121848657453426,133555928335475
%N A053977 Engel expansion of the Euler-Mascheroni constant gamma A001620 = 0.57721566... .
%C A053977 Cf. A006784 for definition of Engel expansion.
%D A053977 F. Engel, Entwicklung der Zahlen nach Stammbruechen, Verhandlungen der 52. Versammlung deutscher Philologen und Schulmaenner in Marburg, 1913, pp. 190-191.
%H A053977 T. D. Noe, <a href="/A053977/b053977.txt">Table of n, a(n) for n=1..300</a>
%H A053977 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 A053977 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 A053977 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EngelExpansion.html">Engel Expansion</a>
%H A053977 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/Euler-MascheroniConstant.html">Euler-Mascheroni Constant</a>
%H A053977 <a href="/index/El#Engel">Index entries for sequences related to Engel expansions</a>
%t A053977 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 A053977 Cf. A006784, A028254, A028257.
%K A053977 nonn,easy,nice
%O A053977 1,1
%A A053977 _Jeppe Stig Nielsen_, Apr 02 2000
%E A053977 More terms and additional comments from _Mitch Harris_, Jan 15 2001