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A235143
Positions of -2 in A235141, the first differences of A234300.
1
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
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
KEYWORD
nonn
AUTHOR
Rajan Murthy, Jan 03 2014
STATUS
approved