A104511 Last 3 digits of the n-th even perfect number.

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.

Links

Table of n, a(n) for n=1..48.

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

Cf. A094540, A000396.

See A000043 for the present state of knowledge about Mersenne primes.

Sequence in context: A325638 A331752 A083387 * A325021 A325025 A325023

Adjacent sequences: A104508 A104509 A104510 * A104512 A104513 A104514

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