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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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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; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| 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
| E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982.
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LINKS
| Harry J. Smith, Table of n, a(n) for n=1..1000
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FORMULA
| a(n+1) = a(n)+A061883(n) = a(n)+A057944(a(n)) = A061885(a(n)) - Henry Bottomley (se16(AT)btinternet.com), May 12 2001
a(n) ~ 0.28276... * 2^n [Charles R Greathouse IV, Jun 19 2011]
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MATHEMATICA
| 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} ]
f[n_]:=Module[{c=Floor[(Sqrt[1+8n]-1)/2]}, (c(c+1))/2]; NestList[#+f[#]&, 1, 40] (* From Harvey P. Dale, June 19 2011 *)
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PROG
| (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]
(Haskell)
a060985 n = a060985_list !! (n-1)
a060985_list = iterate a061885 1 -- Reinhard Zumkeller, Feb 03 2012
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CROSSREFS
| Cf. A060984.
Sequence in context: A018178 A112575 A018079 * A068012 A019138 A154324
Adjacent sequences: A060982 A060983 A060984 * A060986 A060987 A060988
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KEYWORD
| nonn,easy,nice,changed
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AUTHOR
| R. K. Guy (rkg(AT)cpsc.ucalgary.ca), May 11 2001
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EXTENSIONS
| More terms from David W. Wilson (davidwwilson(AT)comcast.net), Henry Bottomley and Robert G. Wilson v, May 12, 2001
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