%I A002973 M0135
%S A002973 1,1,2,1,3,2,1,3,4,4,2,5,5,4,2,5,3,1,5,6,7,1,4,2,8,5,7,8,1,6,7,8,9,4,9,
%T A002973 5,3,10,10,7,6,10,2,5,11,10,5,7,10,12,4,12,9,8,2,11,3,6,13,13,11,1,13,
%U A002973 10,6,11,13,14,7,5,9,2,3,8,10,12,5,14,2,3,14,11,15,16,16,5,15,1,8,11
%N A002973 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.
%C A002973 a(n) is odd iff x^2+y^2==5(mod 8). [From Vladimir Shevelev (shevelev(AT)bgu.ac.il), 
               Jul 12 2009]
%D A002973 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A002973 E. Kogbetliantz and A. Krikorian, Handbook of First Complex Prime Numbers, 
               Gordon and Breach, NY, 1971, p. 243.
%H A002973 T. D. Noe, <a href="b002973.txt">Table of n, a(n) for n=1..1000</a>
%H A002973 S. R. Finch, <a href="http://arXiv.org/abs/math.NT/0701251">Powers of 
               Euler's q-Series</a>, (arXiv:math.NT/0701251).
%e A002973 The 3rd prime of the form 4i+1 is 17=1^2+4^2, so a(3)=4/2=2.
%Y A002973 Cf. A002144, A002972.
%Y A002973 Sequence in context: A115624 A076291 A124458 this_sequence A071476 A071499 
               A039953
%Y A002973 Adjacent sequences: A002970 A002971 A002972 this_sequence A002974 A002975 
               A002976
%K A002973 nonn
%O A002973 1,3
%A A002973 N. J. A. Sloane (njas(AT)research.att.com).
%E A002973 Better description from Jud McCranie (j.mccranie(AT)comcast.net), Mar 
               05 2003