A235387 Positions of 2's in A235141, the first differences of A234300.

3, 7, 9, 13, 15, 17, 19, 21, 25, 29, 31, 35, 37, 39, 41, 43, 45, 47, 51, 53, 55, 57, 59, 63, 67, 69, 71, 73, 75, 79, 81, 83, 89, 91, 93, 95, 97, 99, 101, 103, 105, 113, 115, 117, 121, 123, 125, 127, 129, 131, 135, 141, 143, 145, 147, 151, 153, 155, 157, 161, 165, 167, 169, 175, 177, 179, 181

Offset: 1

Author

Rajan Murthy, Jan 08 2014

Keywords

• nonn

Comments

The positions reflect radii which are a unique sum of two distinct square integers where order doesn't matter.

The positions are more 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 increases 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. This is in contrast to positions where the first difference equals 1 which are exactly balanced by positions which equal -1 .

Examples

			a(2) = 7 corresponding to the shift from squared radius of 4 to (4,5).  This also marks a shift of the radius from 2 to (2,3).  The preceding shift, A235141(6), from radius in the interval (1,2) to 2 and squared radius in the interval (2,4) to 4 does not change the number of edge squares.
a(3) = 9 corresponding to the shift from squared radius of 5 to (5,8).  The radius however remains in the interval (2,3).  The preceding shift, A235141(8), from squared radius in the interval (4,5) to 5 results in a decrease of two due to the completion of the squares with upper right hand corner coordinates of x=1, y =2 and x=2, y=1 (since 5 = 1^2+2^2).
		

Links

• Rajan Murthy, Table of n, a(n) for n = 1..1553

Crossrefs

Cf. A235141, A234300, A235142, A235386.