OFFSET

0,3

COMMENTS

The irrational parts are given in A251631.

The points of the lattice of the Archimedean tiling (4,8,8) lie on certain circles around any point. The length of the regular octagon (8-gon) side is taken as 1 (in some length unit).

The squares of the radii R2(n) of these circles are integers in the real quadratic number field Q(sqrt(2)), hence R2(n) = a(n) + A251631(n)*sqrt(2). The R2 sequence is sorted in increasing order.

LINKS

Wolfdieter Lang, On lattice point circles for the Archimedean tiling (4,8,8).

Wikipedia, Archimedean tilings

EXAMPLE

The first pairs [a(n), A251631(n)] for the squared radii are: [0,0], [1,0], [2,0], [2,1], [3,2], [4,2], [5,2] [6,3], [6,4], [7,4], [9,4], [9,6], [11,6], [10,7], [12,6], [12,8], [13,8], ...

The corresponding radii are (Maple 10 digits if not integer) 0, 1, 1.414213562, 1.847759065, 2.414213562, 2.613125930, 2.797932652, 3.200412581, 3.414213562, 3.557647291, 3.828427124, 4.181540551, 4.414213562, 4.460884994, 4.526066876, 4.828427124, 4.930893276, ...

CROSSREFS

KEYWORD

nonn,easy

AUTHOR

Wolfdieter Lang, Jan 02 2015

STATUS

approved