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

Author

Alfred S. Posamentier (asp2(AT)juno.com) and Robert G. Wilson v, Feb 23 2005

Keywords

• nonn
• base

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.

Crossrefs

Cf. A094540, A000396.

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

Programs

Mathematica

p=MersennePrimeExponent[Range[45]]; Mod[(PowerMod[2, p, 1000] - 1)(PowerMod[2, p - 1, 1000]), 1000] (* edited by Iain Fox, Dec 06 2017 *)

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

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