

A030193


Let S = squares; a(0)=0; a(n) = smallest m such that m  a(i) is not in S for any i < n.


2



0, 2, 5, 7, 10, 12, 15, 17, 20, 22, 34, 39, 44, 52, 57, 62, 65, 67, 72, 85, 95, 109, 119, 124, 127, 130, 132, 137, 142, 147, 150, 170, 177, 180, 182, 187, 192, 197, 204, 210, 215, 238, 243, 249, 255, 257, 260, 262, 267
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OFFSET

0,2


COMMENTS

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


REFERENCES

I. Z. Rusza. Difference sets without squares, Periodica Math. Hugarica 15(1984), 205209.
A. Sárközy. On the difference sets of sequences of integers, Acta. Math. Acad. Sci. Hungar. 31(1978), no. 12, 125149; no. 34, 355386; Ann. Univ. Sci. Budapest. Eotvos Sect. Math. 21(1978), 4553. [Related papers]


LINKS

Karl W. Heuer, Table of n, a(n) for n = 0..61299


MATHEMATICA

moves[n_] := Table[n  i^2, {i, 1, Sqrt[n]}]; gana[n_] := Which[n == 0, False, True, !Select[moves[n], !gana[#] &] =={}]; Select[Range[155]  1, ! gana[#] &] (* _José María grau Ribas_, Jul 19 2013 *)


CROSSREFS

Sequence in context: A038126 A047215 A059536 * A028250 A190087 A182771
Adjacent sequences: A030190 A030191 A030192 * A030194 A030195 A030196


KEYWORD

nonn


AUTHOR

Jan Kristian Haugland (jankrihau(AT)hotmail.com)


EXTENSIONS

More terms from Karl W. Heuer, Jun 13 2013


STATUS

approved



