A328793 Least k such that there exists an equilateral triangle of side length sqrt(A003136(n)) with vertices in an equilateral triangular array of points with k rows.

2, 4, 3, 5, 4, 7, 6, 5, 8, 7, 6, 10, 9, 8, 7, 11, 10, 9, 13, 8, 11, 10, 14, 13, 9, 12, 11, 16, 15, 14, 10, 13, 12, 16, 15, 11, 14, 19, 18, 13, 17, 16, 12, 15, 20, 19, 14, 17, 13, 16, 21, 20, 19, 15, 18, 14, 22, 17, 21, 20, 16, 19, 25, 24, 15, 18, 22, 21, 17

Offset: 1

Author

Peter Kagey, Oct 27 2019

Keywords

• nonn
• look

Comments

a(A024610(n) - 1) = n + 1 for all n > 0, and

a(A024610(n) + k) > n + 1 for all n > 0, k >= 0.

Examples

			For n = 2, there exists an equilateral triangle with side length sqrt(A003136(2)) = sqrt(3) and vertices on equilateral triangular array with a(2) = 4 rows:
     o
    * o
   o o *
  o * o o.
However there is no equilateral triangle of side length sqrt(3) with vertices on a smaller triangular array with three or fewer rows.
		

Links

• Peter Kagey, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A003136, A024610, A328787.