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A235387
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Positions of 2's in A235141, the first differences of A234300.
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1
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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
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OFFSET
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1,1
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COMMENTS
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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 .
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LINKS
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EXAMPLE
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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).
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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