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

1,1

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.

Links

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

Example

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.

Crossrefs

Cf. A235141, A234300, A235142, A235386.

Sequence in context: A230422 A050681 A292867 * A330705 A179186 A349081

Adjacent sequences: A235140 A235141 A235142 * A235144 A235145 A235146

Keyword

nonn

Author

Rajan Murthy, Jan 03 2014

Status

approved