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A231202
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The smallest possible speed in m/s (rounded up) of an object whose relativistic mass is n times its rest mass.
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1
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0, 259627885, 282647041, 290272800, 293735421, 295599350, 296717583, 297441109, 297936141, 298289730, 298551077, 298749699, 298904183, 299026704, 299125511, 299206353, 299273337, 299329458, 299376946, 299417483, 299452365, 299482595, 299508967, 299532109
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OFFSET
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1,2
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COMMENTS
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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.
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REFERENCES
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Lawrence S. Lerner, Physics for Scientists and Engineers, vol. 2, Jones and Bartlett, 1996, p. 1088.
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LINKS
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FORMULA
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a(n) = ceiling(A003678*sqrt(1 - 1/n^2)).
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EXAMPLE
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a(2) = 259627885 because 299792458*sqrt(1 - 1/4) = 259627884.4909793640....
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MATHEMATICA
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c = 299792458; Table[Ceiling[c*Sqrt[1 - 1/n^2]], {n, 24}]
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PROG
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(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)))
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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