A061883 -id:A061883 - cp's OEIS frontend

A060985 a(1) = 1; a(n+1) = a(n) + (largest triangular number <= a(n)).

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

Offset: 1

R. K. Guy, May 11 2001

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.

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

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

Cf. A060984, A237889.

a060985 n = a060985_list !! (n-1)
a060985_list = iterate a061885 1  -- Reinhard Zumkeller, Feb 03 2012

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 *)

{ 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

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

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

A061886 Largest square less than or equal to sum of previous terms.

Original entry on oeis.org

1, 1, 1, 1, 4, 4, 9, 16, 36, 64, 121, 256, 484, 961, 1936, 3844, 7569, 15129, 30276, 60516, 121104, 242064, 483025, 966289, 1932100, 3865156, 7728400, 15452761, 30902481, 61811044, 123609924, 247212729, 494439696, 988850916, 1977669841

Offset: 0

Henry Bottomley, May 12 2001

nonn

			a(6) = 9 since 1+1+1+1+4+4 = 12 and 9 is the largest square less than or equal to this.

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Cf. A061883.

a061886 n = a061886_list !! n
a061886_list = 1 : zipWith (-) (tail a060984_list) a060984_list
-- Reinhard Zumkeller, Dec 24 2013

For n > 0: a(n) = A060984(n+1)-A060984(n) = A048760(A060984(n)).

Formula corrected by Reinhard Zumkeller, Dec 24 2013

cp's OEIS Frontend

A060985 a(1) = 1; a(n+1) = a(n) + (largest triangular number <= a(n)).

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