a(n) is half of the even member of {x,y}, where x^2+y^2 is the n-th prime of the form 4i+1.
1, 1, 2, 1, 3, 2, 1, 3, 4, 4, 2, 5, 5, 4, 2, 5, 3, 1, 5, 6, 7, 1, 4, 2, 8, 5, 7, 8, 1, 6, 7, 8, 9, 4
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Thu Jul 8 19:10:13 CEST 2010 [seqfan] More on A002973 from Karol A. Penson