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A104511
Last 3 digits of the n-th even perfect number.
7
6, 28, 496, 128, 336, 56, 328, 128, 176, 216, 128, 128, 976, 128, 328, 528, 776, 56, 536, 528, 216, 576, 336, 656, 376, 816, 456, 528, 528, 16, 128, 328, 936, 128, 616, 976, 856, 736, 56, 128, 528, 128, 256, 256, 128, 376, 816, 176
OFFSET
1,1
COMMENTS
Whether a perfect number ends in 6 or 28, the preceding digit is odd except for the two initial terms.
All terms except the first two are divisible by 8. - Iain Fox, Dec 06 2017
REFERENCES
Alfred S. Posamentier, Math Charmers, Tantalizing Tidbits for the Mind, Prometheus Books, NY, 2003, page 47.
MATHEMATICA
p=MersennePrimeExponent[Range[45]]; Mod[(PowerMod[2, p, 1000] - 1)(PowerMod[2, p - 1, 1000]), 1000] (* edited by Iain Fox, Dec 06 2017 *)
PROG
(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
CROSSREFS
See A000043 for the present state of knowledge about Mersenne primes.
Sequence in context: A325638 A331752 A083387 * A325021 A325025 A325023
KEYWORD
nonn,base
AUTHOR
Alfred S. Posamentier (asp2(AT)juno.com) and Robert G. Wilson v, Feb 23 2005
EXTENSIONS
Clarified definition and extended by Ivan Panchenko, Aug 05 2014
a(44)-a(45) from Iain Fox, Dec 04 2017
a(46)-a(47) from Ivan Panchenko, Apr 17 2018
a(48) from Iain Fox, Oct 25 2022
STATUS
approved