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 A261544 #61 Feb 16 2025 08:33:26
%S A261544 1,1001,1001001,1001001001,1001001001001,1001001001001001,
%T A261544 1001001001001001001,1001001001001001001001,1001001001001001001001001,
%U A261544 1001001001001001001001001001,1001001001001001001001001001001,1001001001001001001001001001001001
%N A261544 a(n) = Sum_{k=0..n} 1000^k.
%C A261544 A sequence of palindromic numbers.
%H A261544 Colin Barker, <a href="/A261544/b261544.txt">Table of n, a(n) for n = 0..333</a> (corrected by Michel Marcus, Jan 19 2019)
%H A261544 John Rafael M. Antalan, <a href="https://arxiv.org/abs/1908.06014">A Recreational Application of Two Integer Sequences and the Generalized Repetitious Number Puzzle</a>, arXiv:1908.06014 [math.HO], 2019.
%H A261544 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/PalindromicNumber.html">Palindromic Number</a>.
%H A261544 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1001,-1000).
%F A261544 a(n) = (1000^(n + 1) - 1)/999.
%F A261544 a(n) = 1001*a(n-1) - 1000*a(n-2). - _Colin Barker_, Aug 24 2015
%F A261544 G.f.: 1 / ((x-1)*(1000*x-1)). - _Colin Barker_, Aug 24 2015
%F A261544 E.g.f.: (1/999)*(1000000*exp(1000*x) - exp(x)). - _G. C. Greubel_, Aug 29 2015
%e A261544 From _Bruno Berselli_, Aug 25 2015: (Start)
%e A261544 a(n) is the binary representation of A023001
%e A261544 -------------------------------------------------
%e A261544 1 ........................................... 1
%e A261544 1001 ........................................ 9
%e A261544 1001001 ..................................... 73
%e A261544 1001001001 ................................ 585
%e A261544 1001001001001 ............................ 4681
%e A261544 1001001001001001 ........................ 37449
%e A261544 1001001001001001001 .................... 299593
%e A261544 1001001001001001001001 ................ 2396745
%e A261544 1001001001001001001001001 ............ 19173961, etc.
%e A261544 (End)
%t A261544 Table[(1000^(n + 1) - 1)/999, {n, 0, 15}]
%t A261544 LinearRecurrence[{1001, -1000}, {1, 1001}, 20] (* _Vincenzo Librandi_, Aug 24 2015 *)
%o A261544 (PARI) Vec(1 / ((x-1)*(1000*x-1)) + O(x^20)) \\ _Colin Barker_, Aug 24 2015
%o A261544 (Magma) [(1000^(n+1)-1)/999: n in [0..30]]; // _Vincenzo Librandi_, Aug 24 2015
%Y A261544 Cf. A000533, A002113, A023001.
%Y A261544 Subsequence of A033146.
%Y A261544 Sums of 100^k: A094028; sums of 10^k: A000042.
%Y A261544 Cf. similar sequences of the form (k^n-1)/(k-1) listed in A269025.
%K A261544 nonn,base,easy
%O A261544 0,2
%A A261544 _Ilya Gutkovskiy_, Aug 24 2015