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 A017101 #85 Jul 22 2025 15:50:18
%S A017101 3,11,19,27,35,43,51,59,67,75,83,91,99,107,115,123,131,139,147,155,
%T A017101 163,171,179,187,195,203,211,219,227,235,243,251,259,267,275,283,291,
%U A017101 299,307,315,323,331,339,347,355,363,371,379,387,395,403,411,419,427
%N A017101 a(n) = 8n + 3.
%C A017101 Apart from initial term(s), dimension of the space of weight 2n cusp forms for Gamma_0( 47 ).
%C A017101 Also numbers of the form x^2 + y^2 + z^2, where x,y,z are odd integers. - _Alexander Adamchuk_, Dec 01 2006
%C A017101 Conjecture: 2*a(n) is the half-period of oscillation of a Langton's ant colony that is n basic blocks in length. To construct such blocks use a pair of ants facing north at (x,y) and (x+1,y+2) (using Golly's coordinate system). Each successive block is placed 1 cell away from the previous one, i.e., the x coordinate shifts by 3, so we have (x+3k,y) and (x+3k+1,y+2). Also, because of the symmetry of the oscillation pattern, 4*a(n) is the length of the whole period (see MathOverflow link for details). - _Mikhail Kurkov_, Nov 20 2019
%D A017101 James J. Tattersall, Elementary Number Theory in Nine Chapters, Cambridge University Press, 1999, page 247.
%H A017101 Vincenzo Librandi, <a href="/A017101/b017101.txt">Table of n, a(n) for n = 0..5000</a>
%H A017101 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. 5, 14.
%H A017101 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 A017101 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A017101 MathOverflow, <a href="https://mathoverflow.net/q/323164">Absolute oscillator in Langton's ant</a>
%H A017101 William A. Stein, <a href="http://wstein.org/Tables/dimskg0n.gp">Dimensions of the spaces S_k(Gamma_0(N))</a>
%H A017101 William A. Stein, <a href="http://wstein.org/Tables/">The modular forms database</a>
%H A017101 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).
%F A017101 a(n) = A001969(2*n+1) + A001969(2*n) = A000069(2*n+1) + A000069(2*n). - _Philippe Deléham_, Feb 04 2004
%F A017101 G.f.: (3+5*x)/(1-x)^2. - _R. J. Mathar_, Mar 30 2011
%F A017101 a(n) = 2*a(n-1) - a(n-2) for n>1. - _Vincenzo Librandi_, May 28 2011
%F A017101 a(A002265(n)) = A004442(n) + A004443(n). - _Wesley Ivan Hurt_, Apr 06 2016
%F A017101 E.g.f.: exp(x)*(3 + 8*x). - _Stefano Spezia_, Nov 20 2019
%F A017101 a(n) = A004767(2*n), for n >= 0. See also A004767(2*n+1) = A004771(n). - _Wolfdieter Lang_, Feb 03 2022
%p A017101 A017101:=n->8*n+3: seq(A017101(n), n=0..100); # _Wesley Ivan Hurt_, Apr 06 2016
%t A017101 Range[3, 1000, 8] (* _Vladimir Joseph Stephan Orlovsky_, May 27 2011 *)
%t A017101 8*Range[0,80]+3 (* or *) LinearRecurrence[{2,-1},{3,11},80] (* _Harvey P. Dale_, May 04 2023 *)
%o A017101 (Magma) [8*n+3: n in [0..60]]; // _Vincenzo Librandi_, May 28 2011
%o A017101 (PARI) a(n)=8*n+3 \\ _Charles R Greathouse IV_, Jun 02 2013
%Y A017101 Cf. A000069, A001969, A002265, A004442, A004443, A004767, A004771, A004769, A017077, A017089.
%K A017101 nonn,easy
%O A017101 0,1
%A A017101 _N. J. A. Sloane_