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A104803
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a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=1, a(2)=3.
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10
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1, 3, 3, 4, 5, 6, 7, 9, 11, 14, 17, 22, 27, 34, 43, 54, 69, 87, 111, 141, 179, 227, 289, 367, 467, 593, 754, 959, 1219, 1551, 1972, 2508, 3190, 4057, 5160, 6563, 8348, 10618, 13506, 17180, 21853, 27797, 35358, 44976, 57210, 72772, 92567, 117747, 149776
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2)) with a(1)=1, a(2)=3.
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MATHEMATICA
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a[n_]:= a[n]= If[n<3, 2*n-1, Floor[Sqrt[a[n-1]^2 +a[n-2]^2]]]; Table[a[n], {n, 50}] (* Robert G. Wilson v, Mar 28 2005 *)
nxt[{a_, b_}]:={b, Floor[Sqrt[a^2+b^2]]}; Transpose[NestList[nxt, {1, 3}, 50]] [[1]] (* Harvey P. Dale, Oct 29 2012 *)
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PROG
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(Magma)
A104803:= func< n| n lt 3 select (2*n-1) else Floor(Sqrt(Self(n-1)^2 +Self(n-2)^2)) >;
(Sage)
@CachedFunction
def a(n): return (2*n-1) if (n<3) else floor(sqrt(a(n-1)^2 + a(n-2)^2))
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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