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Search: id:A060985
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| A060985 |
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a(1) = 1; a(n+1) = a(n) + (largest triangular number <= a(n)). |
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+0
5
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| 1, 2, 3, 6, 12, 22, 43, 79, 157, 310, 610, 1205, 2381, 4727, 9383, 18699, 37227, 74355, 148660, 296900, 593735, 1187240, 2373810, 4746741, 9491481, 18981027, 37956907, 75910735, 151820416, 303627016, 607253419, 1214497244, 2428978214, 4857918665
(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,...,1000
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FORMULA
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a(n+1) = a(n)+A061883(n) = a(n)+A057944(a(n)) = A061885(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] = Block[ {k = 1}, While[ k*(k + 1)/2 <= a[n - 1], k++ ]; a[n - 1] + k*(k - 1)/2]; Table[ a[n], {n, 1, 40} ]
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PROGRAM
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(PARI) { default(realprecision, 1000); for (n=1, 1000, if (n<2, a=1, k=(sqrt(1 + 8*a) - 1)\2; a+=k*(k + 1)/2 ); write("b060985.txt", n, " ", a) ) } [From Harry J. Smith (hjsmithh(AT)sbcglobal.net), Jul 16 2009]
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CROSSREFS
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Cf. A060984.
Sequence in context: A018178 A112575 A018079 this_sequence A068012 A019138 A154324
Adjacent sequences: A060982 A060983 A060984 this_sequence A060986 A060987 A060988
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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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