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%I #16 May 23 2021 02:43:04
%S 3,4,5,7,9,12,16,22,31,43,60,84,118,166,234,330,466,659,931,1316,1861,
%T 2631,3720,5260,7438,10518,14874,21035,29747,42068,59493,84135,118984,
%U 168268,237966,336534,475930,673066,951859,1346131,1903716,2692260
%N a(n+1) is the integer part of sqrt(2*a(n)^2).
%C A square of side a(n) has a(n+1) as integer part of its diagonal. - _Robert G. Wilson v_, Mar 03 2005
%C Starting the sequence with 0, 1 or 2 would be rather dull.
%H Harvey P. Dale, <a href="/A102822/b102822.txt">Table of n, a(n) for n = 3..1000</a>
%F a(n) ~ c * 2^(n/2), where c = 0.6418844655639201638151389885559421955356352362161057500685561808252532289075... - _Vaclav Kotesovec_, May 23 2021
%e A 3 X 3 square has a diagonal of 4.242640687119285...; the integer part is "4";
%e a 4 X 4 square has a diagonal of 5.656854249492381...; the integer part is "5";
%e a 5 X 5 square has a diagonal of 7.071067811865475...; the integer part is "7";
%e a 7 X 7 square has a diagonal of 9.899494936611665...; the integer part is "9"; etc.
%t NestList[ Function[x, IntegerPart[ Sqrt[ 2x^2]]], 3, 30] (* _Robert G. Wilson v_, Mar 03 2005 *)
%t NestList[IntegerPart[Sqrt[2#^2]]&,3,50] (* _Harvey P. Dale_, Mar 20 2018 *)
%K base,easy,nonn
%O 3,1
%A _Eric Angelini_, Feb 27 2005
%E More terms from _Robert G. Wilson v_, Mar 03 2005
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