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%I A063827 #12 Dec 18 2024 19:45:48
%S A063827 1,2,2,3,4,5,6,8,10,13,16,21,26,33,42,53,68,86,110,140,178,226,288,
%T A063827 366,466,593,754,959,1220,1552,1974,2511,3194,4063,5168,6574,8362,
%U A063827 10637,13530,17211,21892,27847,35422,45057,57314,72904,92736,117962,150050
%N A063827 a(n) = round(sqrt(a(n-2)^2 + a(n-1)^2)) with a(0) = 1 and a(1) = 2.
%C A063827 a(n)/a(n-1) tends towards 1.27201964951... = sqrt((1+sqrt(5))/2). See A139339.
%H A063827 Harry J. Smith, <a href="/A063827/b063827.txt">Table of n, a(n) for n = 0..500</a>
%e A063827 a(7) = 8 since round(sqrt(5^2 + 6^2)) = round(sqrt(61)) = round(7.8102...) = 8.
%t A063827 nxt[{a_,b_}]:={b,Round[Sqrt[a^2+b^2]]}; NestList[nxt,{1,2},50][[;;,1]] (* _Harvey P. Dale_, Dec 18 2024 *)
%o A063827 (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 A063827 Cf. A000283, A139339.
%K A063827 nonn
%O A063827 0,2
%A A063827 _Henry Bottomley_, Aug 20 2001
%E A063827 Missing parenthesis added to definition by _Harry J. Smith_, Sep 01 2009

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