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 A291557 #23 Feb 06 2025 10:38:24
%S A291557 22,45,91,183,367,735,1471,2943,5887,11775,23551,47103,94207,188415,
%T A291557 376831,753663,1507327,3014655,6029311,12058623,24117247,48234495,
%U A291557 96468991,192937983,385875967,771751935,1543503871,3087007743,6174015487,12348030975,24696061951,49392123903,98784247807,197568495615,395136991231,790273982463,1580547964927
%N A291557 a(n) = 23*2^n - 1.
%C A291557 An easy description is: starting from a(0)=22, a(n)=number of integers to be skipped to get a(n+1); i.e., from a(0)=22, skip 22 integers to get a(1)=45; then skip 45 integers to get a(2)=91, etc.
%C A291557 Note that if the initial condition is a(0)=0, a(n)=A000225; if a(0)=2, a(n)=A083329; if a(0)=4, a(n)=A153894, etc.
%H A291557 Michael De Vlieger, <a href="/A291557/b291557.txt">Table of n, a(n) for n = 0..3317</a>
%H A291557 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 A291557 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-2).
%F A291557 From _Chai Wah Wu_, Mar 04 2018: (Start)
%F A291557 a(n) = 3*a(n-1) - 2*a(n-2) for n > 1.
%F A291557 G.f.: (22 - 21*x)/((1 - x)*(1 - 2*x)). (End)
%p A291557 A291557:=n->23*2^n-1: seq(A291557(n), n=0..50); # _Wesley Ivan Hurt_, Oct 05 2017
%t A291557 23*2^Range[0,40]-1 (* or *) LinearRecurrence[{3,-2},{22,45},40] (* _Harvey P. Dale_, Jul 20 2018 *)
%o A291557 (PARI) a(n) = 23*2^n - 1; \\ _Altug Alkan_, Mar 04 2018
%Y A291557 Cf. A000225, A083329, A153894.
%K A291557 nonn,easy
%O A291557 0,1
%A A291557 _Enrique Navarrete_, Aug 26 2017