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A057945
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Number of triangular numbers needed to represent n with greedy algorithm.
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13
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0, 1, 2, 1, 2, 3, 1, 2, 3, 2, 1, 2, 3, 2, 3, 1, 2, 3, 2, 3, 4, 1, 2, 3, 2, 3, 4, 2, 1, 2, 3, 2, 3, 4, 2, 3, 1, 2, 3, 2, 3, 4, 2, 3, 4, 1, 2, 3, 2, 3, 4, 2, 3, 4, 3, 1, 2, 3, 2, 3, 4, 2, 3, 4, 3, 2, 1, 2, 3, 2, 3, 4, 2, 3, 4, 3, 2, 3, 1, 2, 3, 2, 3, 4, 2, 3, 4, 3, 2, 3, 4, 1, 2, 3, 2, 3, 4, 2, 3, 4, 3, 2, 3, 4, 3
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OFFSET
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0,3
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COMMENTS
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The length of (number of moves in) Simon Norton's game in A006019 starting with an initial heap of n if both players always take, never put. - R. J. Mathar, May 13 2016
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LINKS
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FORMULA
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a(0)=0, otherwise a(n)=a(A002262(n))+1.
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EXAMPLE
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a(35)=3 since 35=28+6+1
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MAPLE
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local a, x;
a := 0 ;
x := n ;
while x > 0 do
a := a+1 ;
end do:
a ;
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MATHEMATICA
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A057944[n_] := With[{k = Floor[Sqrt[8n+1]]}, Floor[(k-1)/2]* Floor[(k+1)/2]/2];
a[n_] := Module[{k = 0, x = n}, While[x>0, x = x - A057944[x]; k++]; k];
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PROG
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(Haskell)
a057945 n = g n $ reverse $ takeWhile (<= n) $ tail a000217_list where
g 0 _ = 0
g x (t:ts) = g r ts + a where (a, r) = divMod x t
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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