cp's OEIS Frontend

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

%I A235387 #11 Feb 23 2014 14:43:53
%S A235387 3,7,9,13,15,17,19,21,25,29,31,35,37,39,41,43,45,47,51,53,55,57,59,63,
%T A235387 67,69,71,73,75,79,81,83,89,91,93,95,97,99,101,103,105,113,115,117,
%U A235387 121,123,125,127,129,131,135,141,143,145,147,151,153,155,157,161,165,167,169,175,177,179,181
%N A235387 Positions of 2's in A235141, the first differences of A234300.
%C A235387 The positions reflect radii which are a unique sum of two distinct square integers where order doesn't matter.
%C A235387 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 .
%H A235387 Rajan Murthy, <a href="/A235387/b235387.txt">Table of n, a(n) for n = 1..1553</a>
%e A235387 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.
%e A235387 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).
%Y A235387 Cf. A235141, A234300, A235142, A235386.
%K A235387 nonn
%O A235387 1,1
%A A235387 _Rajan Murthy_, Jan 08 2014