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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 (list; graph; refs; listen; history; text; internal format)
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 f-stop 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 45-45-90 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 n-iterations 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

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Last modified January 20 10:51 EST 2020. Contains 331081 sequences. (Running on oeis4.)