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A104803 a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=1, a(2)=3.

%I A104803 #13 Sep 08 2022 08:45:17
%S A104803 1,3,3,4,5,6,7,9,11,14,17,22,27,34,43,54,69,87,111,141,179,227,289,
%T A104803 367,467,593,754,959,1219,1551,1972,2508,3190,4057,5160,6563,8348,
%U A104803 10618,13506,17180,21853,27797,35358,44976,57210,72772,92567,117747,149776
%N A104803 a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=1, a(2)=3.
%H A104803 G. C. Greubel, <a href="/A104803/b104803.txt">Table of n, a(n) for n = 1..1000</a>
%F A104803 a(n) = floor(sqrt(a(n-1)^2 + a(n-2)^2)) with a(1)=1, a(2)=3.
%t A104803 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 *)
%t A104803 nxt[{a_,b_}]:={b,Floor[Sqrt[a^2+b^2]]}; Transpose[NestList[nxt,{1,3}, 50]] [[1]] (* _Harvey P. Dale_, Oct 29 2012 *)
%o A104803 (Magma)
%o A104803 A104803:= func< n| n lt 3 select (2*n-1) else Floor(Sqrt(Self(n-1)^2 +Self(n-2)^2)) >;
%o A104803 [A104803(n): n in [1..60]]; // _G. C. Greubel_, Jun 27 2021
%o A104803 (Sage)
%o A104803 @CachedFunction
%o A104803 def a(n): return (2*n-1) if (n<3) else floor(sqrt(a(n-1)^2 + a(n-2)^2))
%o A104803 [a(n) for n in (1..60)] # _G. C. Greubel_, Jun 27 2021
%Y A104803 Cf. A104804, A104805, A104810.
%K A104803 nonn
%O A104803 1,2
%A A104803 _Zak Seidov_, Mar 26 2005
%E A104803 More terms from _Robert G. Wilson v_, Mar 28 2005