%I #26 Jun 20 2019 00:13:49

%S 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 53,55,57,59,61,63,65,67,69,71,73,75,77,79,81,83,85,87,89,91,93,95,97,

%U 99,101,103,105,107,109,111,113,115,117,119,121,123,125,127,129,131

%N Odd numbers >= 5.

%C 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 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 Continued fraction expansion of 2/(exp(2)-7). - _Thomas Baruchel_, Nov 04 2003

%C Pisot sequence T(5,7). - _David W. Wilson_

%C 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 F. V. Morley, Proc. Lond. Math. Soc., Jun 1923

%D F. V. Morley, "Inversive Geometry" (George Bell, 1933; reprinted Chelsea Publishing Co. 1954)

%H Ivan Blanco-Chacon, Gary McGuire, and Oisin Robinson, <a href="https://arxiv.org/pdf/1707.06014.pdf">Primes of the form n^2+n+p have density 1</a> (2017)

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H Z. W. Sun, <a href="https://arxiv.org/abs/0803.3737">On sums of primes and triangular numbers</a>, Journal of Combinatorics and Number Theory 1:1 (2009), pp. 65-76.

%H <a href="/index/K#knots">Index entries for sequences related to knots</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (2,-1).

%F a(n) = 2*n + 3.

%F G.f.: x*(5-3*x)/(1-2*x+x^2). a(n) = 2*a(n-1)-a(n-2). - _Colin Barker_, Jan 31 2012

%t Range[5,131,2] (* _Harvey P. Dale_, Aug 11 2012 *)

%o (PARI) a(n)=2*n+3 \\ _Charles R Greathouse IV_, Jul 10 2016

%Y Subsequence of A005408. See A008776 for definitions of Pisot sequences.

%K nonn,easy,nice

%O 1,1

%A _David W. Wilson_

%E Entry revised by _N. J. A. Sloane_, Jan 26 2007