

A020735


Odd numbers >= 5.


3



5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25, 27, 29, 31, 33, 35, 37, 39, 41, 43, 45, 47, 49, 51, 53, 55, 57, 59, 61, 63, 65, 67, 69, 71, 73, 75, 77, 79, 81, 83, 85, 87, 89, 91, 93, 95, 97, 99, 101, 103, 105, 107, 109, 111, 113, 115, 117, 119, 121, 123, 125, 127, 129, 131
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OFFSET

1,1


COMMENTS

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)
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 7sided heptagon, 9sided nonagon, 11gon and 13gon. The 14gon becomes the first to be impossible by either ruler, compass or knotting.
Continued fraction expansion of 2/(exp(2)7).  Thomas Baruchel, Nov 04 2003
Pisot sequence T(5,7).  David W. Wilson
Sun conjectures that any member of this sequence is of the form m^2 + m + p, where p is prime. BlancoChacon, McGuire, & Robinson prove that the primes of this form have density 1.  Charles R Greathouse IV, Jun 20 2019


REFERENCES

F. V. Morley, Proc. Lond. Math. Soc., Jun 1923
F. V. Morley, "Inversive Geometry" (George Bell, 1933; reprinted Chelsea Publishing Co. 1954)


LINKS

Table of n, a(n) for n=1..64.
Ivan BlancoChacon, Gary McGuire, and Oisin Robinson, Primes of the form n^2+n+p have density 1 (2017)
Tanya Khovanova, Recursive Sequences
Z. W. Sun, On sums of primes and triangular numbers, Journal of Combinatorics and Number Theory 1:1 (2009), pp. 6576.
Index entries for sequences related to knots
Index entries for linear recurrences with constant coefficients, signature (2,1).


FORMULA

a(n) = 2*n + 3.
G.f.: x*(53*x)/(12*x+x^2). a(n) = 2*a(n1)a(n2).  Colin Barker, Jan 31 2012


MATHEMATICA

Range[5, 131, 2] (* Harvey P. Dale, Aug 11 2012 *)


PROG

(PARI) a(n)=2*n+3 \\ Charles R Greathouse IV, Jul 10 2016


CROSSREFS

Subsequence of A005408. See A008776 for definitions of Pisot sequences.
Sequence in context: A049013 A267872 A062545 * A329391 A108144 A241835
Adjacent sequences: A020732 A020733 A020734 * A020736 A020737 A020738


KEYWORD

nonn,easy,nice


AUTHOR

David W. Wilson


EXTENSIONS

Entry revised by N. J. A. Sloane, Jan 26 2007


STATUS

approved



