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 A124507 a(n) = floor(exp(n*Pi/2)). 1
 1, 4, 23, 111, 535, 2575, 12391, 59609, 286751, 1379410, 6635623, 31920519, 153552935, 738662922, 3553321280, 17093171648, 82226315585, 395547831244, 1902773895292, 9153250784394, 44031505860632, 211812562992413, 1018919543279304, 4901489415968642 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS In the complex plane, multiplication by i=sqrt(-1) is equivalent to a rotation by 90 degrees (Pi/2 radians) counterclockwise. If one raises the number e=2.718... to the angle in question (i.e., Pi/2, which corresponds to the complex number i), the result is a number 4.81047738... which can be thought of as corresponding (but not being equivalent to) the imaginary unit, i. The next 90-degree sweep, which corresponds to i^2, gives e^Pi = 23.1406... . Continuing around the circle, we find the numbers e^(3*Pi/2) = 111.31..., e^(2*Pi) = 535.4..., etc. Truncating these numbers to integers yields the sequence 1, 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. 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) LINKS G. C. Greubel, Table of n, a(n) for n = 0..1000 Eric Weisstein's World of Mathematics, Euler's Famous Identity. FORMULA a(n) = floor(exp(n*Pi/2)). MAPLE Digits:= 2000: a:= n-> floor(exp(n*Pi/2)): seq(a(n), n=0..30);  # Alois P. Heinz, Nov 25 2018 MATHEMATICA Table[ Floor@ Exp[n*Pi/2], {n, 0, 21}] (* Robert G. Wilson v *) PROG (PARI) vector(30, n, n--; floor(exp(n*Pi/2))) \\ G. C. Greubel, Nov 25 2018 (MAGMA) R:= RealField(10); [Floor(Exp(n*Pi(R)/2)): n in [0..30]]; // G. C. Greubel, Nov 25 2018 (Sage) [floor(exp(n*pi/2)) for n in range(30)] # G. C. Greubel, Nov 25 2018 CROSSREFS Cf. A042972. Sequence in context: A197868 A017973 A306669 * A239813 A174248 A297309 Adjacent sequences:  A124504 A124505 A124506 * A124508 A124509 A124510 KEYWORD nonn AUTHOR Zacariaz Martinez, Dec 27 2006 EXTENSIONS Edited and extended by Robert G. Wilson v, Dec 31 2006 Comments edited by Jon E. Schoenfield, Nov 25 2018 STATUS approved

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Last modified August 26 05:23 EDT 2019. Contains 326328 sequences. (Running on oeis4.)