A231202 The smallest possible speed in m/s (rounded up) of an object whose relativistic mass is n times its rest mass.

0, 259627885, 282647041, 290272800, 293735421, 295599350, 296717583, 297441109, 297936141, 298289730, 298551077, 298749699, 298904183, 299026704, 299125511, 299206353, 299273337, 299329458, 299376946, 299417483, 299452365, 299482595, 299508967, 299532109

Offset: 1

Author

Arkadiusz Wesolowski, Nov 05 2013

Keywords

• nonn
• easy

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.

Examples

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

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
• Wikipedia, Special relativity

Crossrefs

Cf. A003678.

Programs

Magma

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

Mathematica

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

PARI

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

Formula

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