A235143 Positions of -2 in A235141, the first differences of A234300.

8, 14, 16, 20, 24, 26, 28, 30, 34, 38, 40, 42, 44, 50, 52, 54, 56, 62, 66, 68, 70, 74, 78, 80, 82, 86, 88, 90, 92, 94, 96, 98, 100, 104, 112, 114, 120, 122, 124, 126, 128, 130, 134, 136, 140, 142, 144, 146, 150, 152, 156, 160, 164, 166, 168, 172, 174, 176, 178, 180, 182, 184, 188, 190, 196, 200, 204

Offset: 1

Author

Rajan Murthy, Jan 03 2014

Keywords

• nonn

Comments

The positions reflect radii which are a unique sum of two and only two distinct nonzero square integers.

The positions are a bit less frequent in occurrence than the positions where the first differences equal 2 because when the radius changes from exactly an integer value k to the open interval (k,k+1), the number of edge squares increase by 2, while in the reverse case, an increase from the open interval (k,k+1) to exactly k+1, the number of edge squares stays the same rather than decreasing by 2 as occurs in cases when the radii are a sum of two and only two distinct nonzero square integers. This is in contrast to positions where the first difference of A234300 equals 1 which are exactly balanced by positions which equal -1.

Examples

			a(1) = 8 which corresponds to the transition of the square radius from the interval (4,5) to 5 = 1^2 + 2^2.
a(2) = 14 which corresponds to the transition from (9,10) to 10 = 1^2 + 3^2.
		

Links

• Rajan Murthy, Table of n, a(n) for n = 1..1533

Crossrefs

Cf. A235141, A234300, A235142, A235386.