Search: id:A030193
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%I A030193
%S A030193 0,2,5,7,10,12,15,17,20,22,34,39,44,52,57,62,65,67,72,85,95,109,119,
%T A030193 124,127,130,132,137,142,147,150,170,177,180,182,187,192,197,204,
%U A030193 210,215,238,243,249,255,257,260,262,267
%N A030193 Let S = squares; a(0)=0; a(n) = smallest m such that m - a(i) is not 
               in S for any i < n.
%C A030193 Consider the following game: two players make moves in turn, initially 
               the number on the board is n, each move consists of subtracting a 
               perfect square from the number on the board, the player who faces 
               0 loses. This sequence is the set of losing positions in this game. 
               - Mikhail Dvorkin (mikhail.dvorkin(AT)gmail.com), Jan 27 2008
%D A030193 Related papers: A. Sarkozy. On the difference sets of sequences of integers, 
               Acta. Math. Acad. Sci. Hungar. 31(1978), no. 1-2, 125-149; no. 3-4, 
               355-386; Ann. Univ. Sci. Budapest. Eotvos Sect. Math. 21(1978), 45-53.
%D A030193 I. Z. Rusza. Difference sets without squares, Periodica Math. Hugarica 
               15(1984), 205-209.
%Y A030193 Sequence in context: A038126 A047215 A059536 this_sequence A028250 A109260 
               A026340
%Y A030193 Adjacent sequences: A030190 A030191 A030192 this_sequence A030194 A030195 
               A030196
%K A030193 nonn
%O A030193 0,2
%A A030193 Jan Kristian Haugland (jankrihau(AT)hotmail.com)

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