A266685 T(n,k) is the number of loops appearing in pattern of circular arc connecting two vertices of regular polygons. (See Comments.)
1, 2, 1, 1, 2, 1, 4, 1, 1, 2, 3, 2, 1, 6, 1, 1, 2, 1, 4, 1, 2, 1, 8, 1, 1, 2, 1, 2, 5, 2, 1, 2, 1, 10, 1, 1, 2, 3, 4, 1, 6, 1, 4, 3, 2, 1, 12, 1, 1, 2, 1, 2, 1, 2, 7, 2, 1, 2, 1, 2, 1, 14, 1, 1, 2, 1, 4, 1, 2, 1, 8, 1, 2, 1, 4, 1, 2, 1, 16, 1, 1, 2, 3, 2, 1, 6, 1, 2, 9, 2, 1, 6, 1, 2, 3, 2, 1, 18
Offset: 0
Examples
Irregular triangle begins: n\k 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 ... 0 1 2 1 1 2 1 4 2 1 2 3 2 1 6 3 1 2 1 4 1 2 1 8 4 1 2 1 2 5 2 1 2 1 10 5 1 2 3 4 1 6 1 4 3 2 1 12 6 1 2 1 2 1 2 7 2 1 2 1 2 1 14 7 1 2 1 4 1 2 1 8 1 2 1 4 1 2 1 16 ...
Links
- Kival Ngaokrajang, Illustration of initial terms
Programs
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Mathematica
Table[GCD[2 n + 3 + k, k + 1], {n, 0, 8}, {k, 0, 2 n + 1}] // Flatten (* Michael De Vlieger, Jan 03 2016 *) -
PARI
for (n=0, 20,for (k=0, 2*n+2, t=gcd(2*n+3+k, k+1); print1(t, ", ")))
Formula
T(n,k) = gcd(2*n+3+k, k+1), n >= 0, k = 0..2*n+1.
Comments