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A104804 "Rounded hypotenuses": a(n) = round(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=1, a(2)=3.

%I A104804 #17 Oct 08 2018 03:46:26
%S A104804 1,3,3,4,5,6,8,10,13,16,21,26,33,42,53,68,86,110,140,178,226,288,366,
%T A104804 466,593,754,959,1220,1552,1974,2511,3194,4063,5168,6574,8362,10637,
%U A104804 13530,17211,21892,27847,35422,45057,57314,72904,92736,117962,150050
%N A104804 "Rounded hypotenuses": a(n) = round(sqrt(a(n-1)^2 + a(n-2)^2)), a(1)=1, a(2)=3.
%H A104804 Chai Wah Wu, <a href="/A104804/b104804.txt">Table of n, a(n) for n = 1..2000</a>
%F A104804 a(n) = A063827(n) for n > 2. - _Georg Fischer_, Oct 07 2018
%t A104804 a[n_] := a[n] = Round[ Sqrt[ a[n - 1]^2 + a[n - 2]^2]]; a[1] = 1; a[2] = 3; Table[ a[n], {n, 48}] (* _Robert G. Wilson v_, Mar 28 2005 *)
%o A104804 (Python)
%o A104804 from gmpy2 import isqrt_rem
%o A104804 A104804_list = [1,3]
%o A104804 for _ in range(1000):
%o A104804     i, j = isqrt_rem(A104804_list[-1]**2+A104804_list[-2]**2)
%o A104804     A104804_list.append(int(i+ int(4*(j-i) >= 1))) # _Chai Wah Wu_, Aug 16 2016
%Y A104804 Cf. A104803, A104805.
%K A104804 nonn
%O A104804 1,2
%A A104804 _Zak Seidov_, Mar 26 2005
%E A104804 More terms from _Robert G. Wilson v_, Mar 28 2005