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Search: id:A060984
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| A060984 |
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a(1) = 1; a(n+1) = a(n) + (largest square <= a(n)). |
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+0
5
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| 1, 2, 3, 4, 8, 12, 21, 37, 73, 137, 258, 514, 998, 1959, 3895, 7739, 15308, 30437, 60713, 121229, 242333, 484397, 967422, 1933711, 3865811, 7730967, 15459367, 30912128, 61814609, 123625653, 247235577, 494448306, 988888002, 1977738918, 3955408759
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Arises in analyzing `put-or-take' games (see Winning Ways, 484-486, 501-503), the prototype being Epstein's Put-or-Take-a-Square game.
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REFERENCES
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E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982.
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LINKS
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Harry J. Smith, Table of n, a(n) for n=1,...,500
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FORMULA
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a(n+1) = a(n)+[sqrt(a(n))]^2 = a(n)+A061886(n) = a(n)+A048760(a(n)) = A061887(a(n)) - Henry Bottomley (se16(AT)btinternet.com), May 12 2001
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MATHEMATICA
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a[1] = 1; a[n_] := a[n] = a[n - 1] + Floor[ Sqrt[ a[n - 1] ] ]^2; Table[ a[n], {n, 1, 40} ]
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PROGRAM
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(PARI) { default(realprecision, 100); for (n=1, 500, if (n==1, a=1, a+=floor(sqrt(a))^2); write("b060984.txt", n, " ", a); ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 15 2009]
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CROSSREFS
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Cf. A060985.
Sequence in context: A013914 A060200 A057608 this_sequence A098348 A131420 A095705
Adjacent sequences: A060981 A060982 A060983 this_sequence A060985 A060986 A060987
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KEYWORD
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nonn,easy,nice
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AUTHOR
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R. K. Guy (rkg(AT)cpsc.ucalgary.ca), May 11 2001
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EXTENSIONS
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More terms from David W. Wilson (davidwwilson(AT)comcast.net), Henry Bottomley and Robert G. Wilson v, May 12, 2001
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