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 A153894 #49 Feb 04 2025 11:22:38
%S A153894 4,9,19,39,79,159,319,639,1279,2559,5119,10239,20479,40959,81919,
%T A153894 163839,327679,655359,1310719,2621439,5242879,10485759,20971519,
%U A153894 41943039,83886079,167772159,335544319,671088639,1342177279,2684354559
%N A153894 a(n) = 5*2^n - 1.
%C A153894 a(n) is the total number of symbols required in the fully-expanded von Neumann definition of ordinal n + 1, where the string "{}" is used to represent the empty set and spaces are ignored. - _Ely Golden_, Nov 14 2019
%C A153894 a(n) converted to binary is 100 followed by n ones. - _Alexandre Herrera_, Oct 06 2023
%H A153894 Vincenzo Librandi, <a href="/A153894/b153894.txt">Table of n, a(n) for n = 0..1000</a>
%H A153894 Bernard Monjardet, <a href="https://shs.hal.science/halshs-00198635">Acyclic domains of linear orders: a survey</a>, in "The Mathematics of Preference, Choice and Order: Essays in Honor of Peter Fishburn", edited by Steven Brams, William V. Gehrlein and Fred S. Roberts, Springer, 2009, pp. 139-160. This version: <halshs-00198635>. - _N. J. A. Sloane_, Feb 07 2009
%H A153894 Gennady Eremin, <a href="https://arxiv.org/abs/2405.16143">Partitioning the set of natural numbers into Mersenne trees and into arithmetic progressions; Natural Matrix and Linnik's constant</a>, arXiv:2405.16143 [math.CO], 2024. See pp. 3-5, 14.
%H A153894 Gennady Eremin, <a href="https://arxiv.org/abs/2501.17090">Infinite matrix of odd natural numbers. A bit about Sophie Germain prime numbers</a>, arXiv:2501.17090 [math.GM], 2025. See pp. 3, 11.
%H A153894 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A153894 a(n) = 2*a(n-1) + 1, n>0.
%F A153894 a(n) = A052549(n+1).
%F A153894 G.f.: (4 - 3*x) / ( (2*x-1)*(x-1) ). - _R. J. Mathar_, Oct 22 2011
%F A153894 a(n) + a(n-1)^2 = A309779(n), a perfect square. - _Vincenzo Librandi_, Oct 28 2011
%F A153894 From _G. C. Greubel_, Sep 01 2016: (Start)
%F A153894 a(n) = 3*a(n-1) - 2*a(n-2).
%F A153894 E.g.f.: 5*exp(2*x) - exp(x). (End)
%t A153894 a=4;lst={a};Do[a=a*2+1;AppendTo[lst,a],{n,5!}];lst
%t A153894 LinearRecurrence[{3,-2},{4,9}, 25] (* or *) Table[5*2^n - 1, {n,0,25}] (* _G. C. Greubel_, Sep 01 2016 *)
%o A153894 (Magma) [5*2^n-1: n in [0..30]]; // _Vincenzo Librandi_, Oct 28 2011
%o A153894 (PARI) a(n)=5*2^n-1 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A153894 Cf. A052549, A309779.
%K A153894 nonn,easy
%O A153894 0,1
%A A153894 _Vladimir Joseph Stephan Orlovsky_, Jan 03 2009
%E A153894 Edited by _N. J. A. Sloane_, Feb 07 2009
%E A153894 Definition corrected by _Franklin T. Adams-Watters_, Apr 22 2009