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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 (list; graph; refs; listen; history; text; internal format)
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), 205-209.

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. [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

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Last modified July 25 02:58 EDT 2014. Contains 244897 sequences.