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A124507
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Floor(e^(n*Pi/2)).
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0
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1, 4, 23, 111, 535, 2575, 12391, 59609, 286751, 1379410, 6635623, 31920519, 153552935, 738662922, 3553321280, 17093171648, 82226315585, 395547831244, 1902773895292, 9153250784394, 44031505860632, 211812562992413
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| If one considers rotations in the complex plane the complex number i can be thought of as a rotation by 90 degrees counterclockwise. This also corresponds to half of pi. If one raises the number e (2.718...) to the angle in question, (that angle corresponding to the complex number i, or half of pi), the result is an number 4.81047738... which can be thought of as corresponding (but not being equivalent to) the complex number, i.
The next 90 degree sweep, which corresponds to i^2, is 23.1406... and is the known constant, e^pi. Continuing around the circle, we find the numbers i^3 = 111.31..., i^4 = 535.4... etc. Truncating these numbers to integers yields the series, 0, 4, 23, 111, etc. I came across this sequence as I tried to find a real number that corresponded to the complex number 'i' in the complex plane.
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REFERENCES
| Frank Ayres, Jr., Robert E. Moyer and Murray R. Spiegel, "Essential Trigonometry and Algebra for University Students" (?) (1999), p. 3.
Roger Penrose, The Road to Reality (?) (2005), p. 88 (figure 5.3)
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LINKS
| Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics,Euler's Famous Identity.
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FORMULA
| e^(i*Pi)+1=0 <==> i=e^(i*Pi/2). Therefore i^n can imply e^(n*i*Pi/2).
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MATHEMATICA
| Table[ Floor@ Exp[n*Pi/2], {n, 0, 21}] (* Robert G. Wilson v *)
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CROSSREFS
| Cf. A042972.
Sequence in context: A082970 A197868 A017973 * A174248 A201350 A015532
Adjacent sequences: A124504 A124505 A124506 * A124508 A124509 A124510
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KEYWORD
| nonn
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AUTHOR
| Zacariaz Martinez (euneirophrenia(AT)gmail.com), Dec 27 2006
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EXTENSIONS
| Edited and extended by Robert G. Wilson v (rgwv(AT)rgwv.com), Dec 31 2006
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