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A017910
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Powers of sqrt(2) rounded down.
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12
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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; internal format)
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OFFSET
| 0,3
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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
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..1000
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MAPLE
| A017910 := n->floor(sqrt(2^n)); # Peter Luschny, Sep 20 2011
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MATHEMATICA
| Floor[(Sqrt[2])^Range[0, 40]] (* Vincenzo Librandi, Nov 20 2011 *)
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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
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CROSSREFS
| Cf. A136417. Bisections: A000079, A084188.
Sequence in context: A157162 A109434 A089299 * A013979 A107458 A060280
Adjacent sequences: A017907 A017908 A017909 * A017911 A017912 A017913
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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