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A060985 a(1) = 1; a(n+1) = a(n) + (largest triangular number <= a(n)). 6
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; text; internal format)
OFFSET

1,2

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.

REFERENCES

E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982.

LINKS

Harry J. Smith, Table of n, a(n) for n = 1..1000

FORMULA

a(n+1) = a(n) + A061883(n) = a(n) + A057944(a(n)) = A061885(a(n)). - Henry Bottomley, May 12 2001

a(n) ~ 0.28276... * 2^n. - Charles R Greathouse IV, Jun 19 2011

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] (* Harvey P. Dale, Jun 19 2011 *)

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) ) } \\ Harry J. Smith, Jul 16 2009

(Haskell)

a060985 n = a060985_list !! (n-1)

a060985_list = iterate a061885 1  -- Reinhard Zumkeller, Feb 03 2012

CROSSREFS

Cf. A060984, A237889.

Sequence in context: A112575 A018079 A289920 * A068012 A261930 A019138

Adjacent sequences:  A060982 A060983 A060984 * A060986 A060987 A060988

KEYWORD

nonn,easy,nice

AUTHOR

R. K. Guy, May 11 2001

EXTENSIONS

More terms from David W. Wilson, Henry Bottomley and Robert G. Wilson v, May 12 2001

STATUS

approved

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Last modified January 18 00:50 EST 2022. Contains 350410 sequences. (Running on oeis4.)