A063827 a(n) = round(sqrt(a(n-2)^2 + a(n-1)^2)) with a(0) = 1 and a(1) = 2.

1, 2, 2, 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

0,2

Comments

a(n)/a(n-1) tends towards 1.27201964951... = sqrt((1+sqrt(5))/2). See A139339.

Links

Harry J. Smith, Table of n, a(n) for n = 0..500

Example

a(7) = 8 since round(sqrt(5^2 + 6^2)) = round(sqrt(61)) = round(7.8102...) = 8.

Mathematica

nxt[{a_, b_}]:={b, Round[Sqrt[a^2+b^2]]}; NestList[nxt, {1, 2}, 50][[;; , 1]] (* Harvey P. Dale, Dec 18 2024 *)

Prog

(PARI) { default(realprecision, 50); for (n=0, 500, if (n>1, a=round(sqrt(a2^2 + a1^2)); a2=a1; a1=a, if (n, a=a1=2, a=a2=1)); write("b063827.txt", n, " ", a) ) } \\ Harry J. Smith, Sep 01 2009

Crossrefs

Cf. A000283, A139339.

Sequence in context: A316081 A238708 A266751 * A241651 A127217 A240735

Adjacent sequences: A063824 A063825 A063826 * A063828 A063829 A063830

Keyword

nonn

Author

Henry Bottomley, Aug 20 2001

Extensions

Missing parenthesis added to definition by Harry J. Smith, Sep 01 2009

Status

approved