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A231202 The smallest possible speed in m/s (rounded up) of an object whose relativistic mass is n times its rest mass. 1
0, 259627885, 282647041, 290272800, 293735421, 295599350, 296717583, 297441109, 297936141, 298289730, 298551077, 298749699, 298904183, 299026704, 299125511, 299206353, 299273337, 299329458, 299376946, 299417483, 299452365, 299482595, 299508967, 299532109 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

First compute s(n) = c*sqrt(1 - 1/n^2), where c = 299792458 is the speed of light in vacuum (m/s). Then round up. Note that a(n) = c for n >= 12244, which implies that lim n -> infinity s(n) = c.

REFERENCES

Lawrence S. Lerner, Physics for Scientists and Engineers, vol. 2, Jones and Bartlett, 1996, p. 1088.

LINKS

Table of n, a(n) for n=1..24.

Albert Einstein, Zur Elektrodynamik bewegter K├Ârper, Annalen der Physik, vol. 322, Issue 10, pp. 891-921. [gallica]

Wikipedia, Albert Einstein

Wikipedia, Special relativity

FORMULA

a(n) = ceiling(A003678*sqrt(1 - 1/n^2)).

EXAMPLE

a(2) = 259627885 because 299792458*sqrt(1 - 1/4) = 259627884.4909793640....

MATHEMATICA

c = 299792458; Table[Ceiling[c*Sqrt[1 - 1/n^2]], {n, 24}]

PROG

(MAGMA) c:=299792458; [Ceiling(c*Sqrt(1-1/n^2)) : n in [1..24]]

(PARI) c=299792458; vector(24, n, ceil(c*sqrt(1-1/n^2)))

CROSSREFS

Cf. A003678.

Sequence in context: A204415 A246224 A205934 * A226448 A250433 A125576

Adjacent sequences:  A231199 A231200 A231201 * A231203 A231204 A231205

KEYWORD

nonn,easy

AUTHOR

Arkadiusz Wesolowski, Nov 05 2013

STATUS

approved

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Last modified September 21 00:17 EDT 2019. Contains 327252 sequences. (Running on oeis4.)