cp's OEIS Frontend

From Wolfdieter Lang, Mar 30 2018: (Start)

a(k) + 2 =: s(k) is used to obtain for 2^s(k)*vec v_{-k} integer components in the quadratic number field Q(sqrt(3)), where vec v_{-k} = vec(O_{-(k+1)}, O_{-k})) with the centers O_{-k}, k >= 0, for a k-family of regular hexagons H_{-k} forming part of a discrete spiral. See the linked paper, Lemma 4 and Table 7.

a(k+2) =: v0(k), k >= 0, based on the sequence A300290, is used to obtain for

2^(v0(k))*V_{-k}(0) as well as 2^(v0(k))*V_{-k}(3) integer coordinates in the quadratic number field Q(sqrt(3)), where V_{-k}(j), j = 0..5, are the vertices of the regular hexagon H_{-k}, of the above mentioned k-family. See the linked paper, Lemma 6 and Table 8.

a(k+1) + 1 =: v1(k), k >= 1, is used to obtain for 2^(v1(k))*V_{-k}(1) as well as 2^(v1(k))*V_{-k}(4) integer coordinates in the quadratic number field Q(sqrt(3)), with vertices V_{-k}(j) of H_{-k}. See the linked paper, Lemma 6 and Table 9.

(End)