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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
Albert Einstein, Zur Elektrodynamik bewegter Körper, Annalen der Physik, vol. 322, Issue 10, pp. 891-921. [gallica]
Wikipedia, Albert Einstein
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 A329464
KEYWORD
nonn,easy
AUTHOR
STATUS
approved

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Last modified February 23 11:40 EST 2024. Contains 370283 sequences. (Running on oeis4.)