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 A091832 #38 Jan 05 2025 19:51:37
%S A091832 7,18,19,136,349,357,1354,6996,7135,9531,11558,15996,17432,52118,
%T A091832 151048,427802,821834,877819,972918,1046690,1540789,3653077,8200738,
%U A091832 9628573,164153335,5607624822,86457467082,141885251873,151882622551
%N A091832 Pierce expansion of 1/e^2.
%C A091832 If u(0) = exp(1/m) with m an integer >= 1 and u(n+1) = u(n)/frac(u(n)) then floor(u(n)) = m*n.
%H A091832 G. C. Greubel, <a href="/A091832/b091832.txt">Table of n, a(n) for n = 1..501</a> [a(1)=7 inserted by Georg Fischer, Nov 20 2020]
%H A091832 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. Théor. Nombres Bordeaux (2) 3 (1991), no. 1, 43-53.
%H A091832 Vlado Keselj, <a href="https://cs.uwaterloo.ca/research/tr/1996/21/cs-96-21.pdf">Length of Finite Pierce Series: Theoretical Analysis and Numerical Computations </a>.
%H A091832 Jeffrey Shallit, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/22-4/shallit1.pdf">Some predictable Pierce expansions</a>, Fib. Quart., 22 (1984), 332-335.
%H A091832 Pelegrí Viader, Lluís Bibiloni, and Jaume Paradís, <a href="http://dx.doi.org/10.2139/ssrn.145561">On a problem of Alfred Renyi</a>, Economics Working Paper No. 340.
%F A091832 Let u(0) = exp(2) and u(n+1) = u(n)/frac(u(n)) where frac(x) is the fractional part of x, then a(n) = floor(u(n)).
%F A091832 1/e^2 = 1/a(1) - 1/(a(1)*a(2)) + 1/(a(1)*a(2)*a(3)) - 1/(a(1)*a(2)*a(3)*a(4)) ...
%F A091832 Limit_{n->oo} a(n)^(1/n) = e.
%t A091832 PierceExp[A_, n_] := Join[Array[1 &, Floor[A]], First@Transpose@ NestList[{Floor[1/Expand[1 - #[[1]] #[[2]]]], Expand[1 - #[[1]] #[[2]]]} &, {Floor[1/(A - Floor[A])], A - Floor[A]}, n - 1]]; PierceExp[N[1/E^2, 7!], 15] (* _G. C. Greubel_, Nov 14 2016 *)
%o A091832 (PARI) default(realprecision, 100000); r=exp(2); for(n=1, 100, s=(r/(r-floor(r))); print1(floor(r), ", "); r=s) \\ _Benoit Cloitre_ [amended by _Georg Fischer_, Nov 20 2020]
%Y A091832 Cf. A006275, A006276, A006283.
%Y A091832 Cf. A006784 (Pierce expansion definition), A059194.
%K A091832 nonn
%O A091832 1,1
%A A091832 _Benoit Cloitre_, Mar 09 2004
%E A091832 a(1)=7 inserted by _Georg Fischer_, Nov 20 2020