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

1, 3, 3, 4, 5, 6, 8, 10, 13, 16, 21, 26, 33, 42, 53, 68, 86, 110, 140, 178, 226, 288, 366, 466, 593, 754, 959, 1220, 1552, 1974, 2511, 3194, 4063, 5168, 6574, 8362, 10637, 13530, 17211, 21892, 27847, 35422, 45057, 57314, 72904, 92736, 117962, 150050

Offset: 1

Author

Zak Seidov, Mar 26 2005

Keywords

• nonn

Links

• Chai Wah Wu, Table of n, a(n) for n = 1..2000

Crossrefs

Cf. A104803, A104805.

Programs

Mathematica

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 *)

Python

from gmpy2 import isqrt_rem
A104804_list = [1,3]
for _ in range(1000):
    i, j = isqrt_rem(A104804_list[-1]**2+A104804_list[-2]**2)
    A104804_list.append(int(i+ int(4*(j-i) >= 1))) # Chai Wah Wu, Aug 16 2016

Formula

a(n) = A063827(n) for n > 2. - Georg Fischer, Oct 07 2018

Extensions

More terms from Robert G. Wilson v, Mar 28 2005