

A017910


Powers of sqrt(2) rounded down.


22



1, 1, 2, 2, 4, 5, 8, 11, 16, 22, 32, 45, 64, 90, 128, 181, 256, 362, 512, 724, 1024, 1448, 2048, 2896, 4096, 5792, 8192, 11585, 16384, 23170, 32768, 46340, 65536, 92681, 131072, 185363, 262144, 370727, 524288
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OFFSET

0,3


COMMENTS

a(n) is the number of positive squares <= 2^n (cf. A136417).  Hans Havermann, Apr 05 2008
If expressed to two significant figures, these are the fstop numbers in photography: 1, 1.4, 2, 2.8, 4, 5.6, 8, 11, 16, 22 ...
There are also "half stops" (sqrt(2)^(n/2)) and
"third stops" (sqrt(2)^(n/3)):1, 1.4, 1.6, 1.8, 2.0, 2.2, 2.5, 2.8, 3.2, 3.6, 4, 4.5, 5, 5.7, 6.3, 7.1, 8, 9, 10
a(n) is also the ratio of circles curvature (rounded down) inscribed in 454590 triangle arranged as spiral form. See illustration in links.  Kival Ngaokrajang, Aug 28 2013
a(n) is also the total length of Heighway dragon (rounded down) after niterations when L(0) = 1. See illustration in links.  Kival Ngaokrajang, Dec 15 2013


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Kival Ngaokrajang, Illustration of initial terms
Kival Ngaokrajang, Illustration of Heighway dragon for n = 0..5
Wikipedia, Dragon curve


FORMULA

a(n) = A000196(A000079(n)).  Jason Kimberley, Oct 28 2016


MAPLE

A017910 := n>floor(sqrt(2^n)); # Peter Luschny, Sep 20 2011


MATHEMATICA

Floor[(Sqrt[2])^Range[0, 40]] (* Vincenzo Librandi, Nov 20 2011 *)


PROG

(PARI) a(n)=sqrtint(2^n) \\ Charles R Greathouse IV, Sep 22 2011
(MAGMA) [Floor(Sqrt(2^n)): n in [0..40]]; // Vincenzo Librandi, Nov 20 2011
(MAGMA) [Isqrt(2^n):n in[0..40]]; // Jason Kimberley, Oct 25 2016


CROSSREFS

Cf. A136417. Bisections: A000079, A084188.
Sequence in context: A157162 A109434 A089299 * A240734 A328460 A238478
Adjacent sequences: A017907 A017908 A017909 * A017911 A017912 A017913


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane.


STATUS

approved



