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 A020735 #32 Jun 16 2025 08:41:20 %S A020735 5,7,9,11,13,15,17,19,21,23,25,27,29,31,33,35,37,39,41,43,45,47,49,51, %T A020735 53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97, %U A020735 99,101,103,105,107,109,111,113,115,117,119,121,123,125,127,129,131 %N A020735 Odd numbers >= 5. %C A020735 Values of n such that a regular polygon with n sides can be formed by tying knots in a strip of paper. - Robert A. J. Matthews (rajm(AT)compuserve.com) %C A020735 These polygons fill in many of the gaps left by the Greeks, who were restricted to compass and ruler. Specifically, they make possible construction of the regular 7-sided heptagon, 9-sided nonagon, 11-gon and 13-gon. The 14-gon becomes the first to be impossible by either ruler, compass or knotting. %C A020735 Continued fraction expansion of 2/(exp(2)-7). - _Thomas Baruchel_, Nov 04 2003 %C A020735 Pisot sequence T(5,7). - _David W. Wilson_ %C A020735 Sun conjectures that any member of this sequence is of the form m^2 + m + p, where p is prime. Blanco-Chacon, McGuire, & Robinson prove that the primes of this form have density 1. - _Charles R Greathouse IV_, Jun 20 2019 %D A020735 F. V. Morley, Proceedings of the London Mathematical Society, Jun 1923. %D A020735 F. V. Morley, "Inversive Geometry" (George Bell, 1933; reprinted Chelsea Publishing Co. 1954). %H A020735 Ivan Blanco-Chacon, Gary McGuire, and Oisin Robinson, <a href="https://arxiv.org/abs/1707.06014">Primes of the form n^2+n+p have density 1</a>, arXiv:1707.06014 [math.NT], 2017. %H A020735 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>. %H A020735 Zhi-Wei Sun, <a href="https://arxiv.org/abs/0803.3737">On sums of primes and triangular numbers</a>, arXiv:0803.3737 [math.NT], 2008-2009; Journal of Combinatorics and Number Theory 1:1 (2009), pp. 65-76. %H A020735 <a href="/index/K#knots">Index entries for sequences related to knots</a>. %H A020735 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1). %F A020735 a(n) = 2*n + 3. %F A020735 From _Colin Barker_, Jan 31 2012: (Start) %F A020735 G.f.: x*(5-3*x)/(1-2*x+x^2). %F A020735 a(n) = 2*a(n-1) - a(n-2). (End) %F A020735 From _Elmo R. Oliveira_, Oct 31 2024: (Start) %F A020735 E.g.f.: exp(x)*(2*x + 3) - 3. %F A020735 a(n) = A016825(n+1)/2 = A028347(n+2) - A028347(n+1). (End) %t A020735 Range[5,131,2] (* _Harvey P. Dale_, Aug 11 2012 *) %o A020735 (PARI) a(n)=2*n+3 \\ _Charles R Greathouse IV_, Jul 10 2016 %Y A020735 Subsequence of A005408. See A008776 for definitions of Pisot sequences. %Y A020735 Cf. A016825, A028347. %K A020735 nonn,easy,nice %O A020735 1,1 %A A020735 _David W. Wilson_ %E A020735 Entry revised by _N. J. A. Sloane_, Jan 26 2007