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

%I A060985 #31 Jul 03 2018 02:27:33
%S A060985 1,2,3,6,12,22,43,79,157,310,610,1205,2381,4727,9383,18699,37227,
%T A060985 74355,148660,296900,593735,1187240,2373810,4746741,9491481,18981027,
%U A060985 37956907,75910735,151820416,303627016,607253419,1214497244,2428978214,4857918665
%N A060985 a(1) = 1; a(n+1) = a(n) + (largest triangular number <= a(n)).
%C A060985 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.
%D A060985 E. R. Berlekamp, J. H. Conway and R. K. Guy, Winning Ways, Academic Press, NY, 2 vols., 1982.
%H A060985 Harry J. Smith, <a href="/A060985/b060985.txt">Table of n, a(n) for n = 1..1000</a>
%F A060985 a(n+1) = a(n) + A061883(n) = a(n) + A057944(a(n)) = A061885(a(n)). - _Henry Bottomley_, May 12 2001
%F A060985 a(n) ~ 0.28276... * 2^n. - _Charles R Greathouse IV_, Jun 19 2011
%t A060985 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} ]
%t A060985 f[n_]:=Module[{c=Floor[(Sqrt[1+8n]-1)/2]},(c(c+1))/2]; NestList[#+f[#]&, 1, 40] (* _Harvey P. Dale_, Jun 19 2011 *)
%o A060985 (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
%o A060985 (Haskell)
%o A060985 a060985 n = a060985_list !! (n-1)
%o A060985 a060985_list = iterate a061885 1  -- _Reinhard Zumkeller_, Feb 03 2012
%Y A060985 Cf. A060984, A237889.
%K A060985 nonn,easy,nice
%O A060985 1,2
%A A060985 _R. K. Guy_, May 11 2001
%E A060985 More terms from _David W. Wilson_, _Henry Bottomley_ and _Robert G. Wilson v_, May 12 2001