A102822 a(n+1) is the integer part of sqrt(2*a(n)^2).

3, 4, 5, 7, 9, 12, 16, 22, 31, 43, 60, 84, 118, 166, 234, 330, 466, 659, 931, 1316, 1861, 2631, 3720, 5260, 7438, 10518, 14874, 21035, 29747, 42068, 59493, 84135, 118984, 168268, 237966, 336534, 475930, 673066, 951859, 1346131, 1903716, 2692260

Offset

3,1

Comments

A square of side a(n) has a(n+1) as integer part of its diagonal. - Robert G. Wilson v, Mar 03 2005

Starting the sequence with 0, 1 or 2 would be rather dull.

Links

Harvey P. Dale, Table of n, a(n) for n = 3..1000

Formula

a(n) ~ c * 2^(n/2), where c = 0.6418844655639201638151389885559421955356352362161057500685561808252532289075... - Vaclav Kotesovec, May 23 2021

Example

A 3 X 3 square has a diagonal of 4.242640687119285...; the integer part is "4";
a 4 X 4 square has a diagonal of 5.656854249492381...; the integer part is "5";
a 5 X 5 square has a diagonal of 7.071067811865475...; the integer part is "7";
a 7 X 7 square has a diagonal of 9.899494936611665...; the integer part is "9"; etc.

Mathematica

NestList[ Function[x, IntegerPart[ Sqrt[ 2x^2]]], 3, 30] (* Robert G. Wilson v, Mar 03 2005 *)
NestList[IntegerPart[Sqrt[2#^2]]&, 3, 50] (* Harvey P. Dale, Mar 20 2018 *)

Crossrefs

Sequence in context: A035249 A104805 A260996 * A346986 A167159 A226918

Adjacent sequences: A102819 A102820 A102821 * A102823 A102824 A102825

Keyword

base,easy,nonn

Author

Eric Angelini, Feb 27 2005

Extensions

More terms from Robert G. Wilson v, Mar 03 2005

Status

approved