A063827 - OEIS

%I #10 Jun 25 2018 03:22:55

%S 1,2,2,3,4,5,6,8,10,13,16,21,26,33,42,53,68,86,110,140,178,226,288,

%T 366,466,593,754,959,1220,1552,1974,2511,3194,4063,5168,6574,8362,

%U 10637,13530,17211,21892,27847,35422,45057,57314,72904,92736,117962,150050

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

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

%H Harry J. Smith, <a href="/A063827/b063827.txt">Table of n, a(n) for n = 0..500</a>

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

%o (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

%Y Cf. A000283, A139339.

%K nonn

%O 0,2

%A _Henry Bottomley_, Aug 20 2001

%E Missing parenthesis added to definition by _Harry J. Smith_, Sep 01 2009