|
%I #35 Oct 25 2022 17:23:41
%S 6,28,496,128,336,56,328,128,176,216,128,128,976,128,328,528,776,56,
%T 536,528,216,576,336,656,376,816,456,528,528,16,128,328,936,128,616,
%U 976,856,736,56,128,528,128,256,256,128,376,816,176
%N Last 3 digits of the n-th even perfect number.
%C Whether a perfect number ends in 6 or 28, the preceding digit is odd except for the two initial terms.
%C All terms except the first two are divisible by 8. - _Iain Fox_, Dec 06 2017
%D Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 47.
%t p=MersennePrimeExponent[Range[45]]; Mod[(PowerMod[2, p, 1000] - 1)(PowerMod[2, p - 1, 1000]), 1000] (* edited by _Iain Fox_, Dec 06 2017 *)
%o (PARI) a(p) = lift(Mod((Mod(2, 1000)^p - 1)*Mod(2, 1000)^(p-1), 1000)) \\ (where p is the n-th Mersenne exponent A000043) _Iain Fox_, Dec 04 2017
%Y Cf. A094540, A000396.
%Y See A000043 for the present state of knowledge about Mersenne primes.
%K nonn,base
%O 1,1
%A Alfred S. Posamentier (asp2(AT)juno.com) and _Robert G. Wilson v_, Feb 23 2005
%E Clarified definition and extended by _Ivan Panchenko_, Aug 05 2014
%E a(44)-a(45) from _Iain Fox_, Dec 04 2017
%E a(46)-a(47) from _Ivan Panchenko_, Apr 17 2018
%E a(48) from _Iain Fox_, Oct 25 2022
|
