A262770 A Beatty sequence: a(n)=floor(n*p) where p=2*cos(Pi/7)=A160389.

0, 1, 3, 5, 7, 9, 10, 12, 14, 16, 18, 19, 21, 23, 25, 27, 28, 30, 32, 34, 36, 37, 39, 41, 43, 45, 46, 48, 50, 52, 54, 55, 57, 59, 61, 63, 64, 66, 68, 70, 72, 73, 75, 77, 79, 81, 82, 84, 86, 88, 90, 91, 93, 95, 97, 99, 100, 102, 104, 106, 108, 109, 111, 113, 115, 117, 118, 120, 122, 124, 126, 127, 129, 131, 133, 135, 136, 138, 140, 142, 144, 145, 147, 149, 151, 153, 154, 156, 158, 160, 162, 163, 165, 167, 169, 171, 172, 174, 176, 178, 180, 181, 183, 185, 187, 189, 191

Offset: 0

Author

Patrick D McLean, Sep 30 2015

Keywords

• nonn

Comments

Beatty sequence of the shorter diagonal (A160389) in a regular heptagon with sidelength 1.

Complement of Beatty sequence A262773 of the longer diagonal (A231187) in a regular heptagon with sidelength 1.

First 106 terms agree with A187318, but A187318(106)=190 while A262770(106)=191.

Links

• Peter Steinbach, Golden Fields: A Case for the Heptagon, Mathematics Magazine, Vol. 70, No. 1, Feb. 1997.
• Index entries for sequences related to Beatty sequences

Crossrefs

Complement of A262773.

Initially agrees with A187318 (because 2*cos(Pi/7) is close to 9/5).

Programs

Mathematica

Table[Floor[2 n Cos[Pi/7]], {n, 0, 106}] (* Michael De Vlieger, Oct 05 2015 *)

Octave

p=roots([1,-1,-2,1])(1); a(n)=floor(p*n)

PARI

a(n) = floor(n*2*cos(Pi/7)); \\ Michel Marcus, Oct 05 2015