A094540 Last digit of the n-th perfect number.

6, 8, 6, 8, 6, 6, 8, 8, 6, 6, 8, 8, 6, 8, 8, 8, 6

Offset: 1

Author

Eric W. Weisstein, May 08 2004

Keywords

• nonn
• hard
• base

Comments

Conjecture: Ratio of 6's to 8's approaches 1.5 as a limit as this sequence approaches infinity. - J. Lowell, Jun 26 2007

Since the best known lower bound for odd perfect numbers is ca. 10^1500, I removed all terms after a(17). - Ivan Panchenko, Sep 16 2014

References

• David Wells, The Penguin Dictionary of Curious and Interesting Numbers. Penguin Books, NY, 1986, Revised edition 1987. See p. 107.

Links

• Math Forum at Drexel, List of Perfect Numbers.
• Eric Weisstein's World of Mathematics, Perfect Number.

Crossrefs

Cf. A000396. See A000043 for the present state of knowledge about Mersenne primes.

Programs

Maple

# (Maple code from N. J. A. Sloane)
# let s1 := list of terms in A000043
f:=n->if n mod 4 = 0 then 4 else n mod 4; fi; g:= x->2^f(x-1)*(2^f(x)-1); map(g,s1);

Mathematica

p={ the list of the Mersenne exponents (A000043) }; Mod[(PowerMod[2, p, 10] - 1)(PowerMod[2, p - 1, 10]), 10] (* Robert G. Wilson v, May 23 2004 *)

Extensions

Edited by N. J. A. Sloane, Apr 01 2008, at the suggestion of Ant King and Omar E. Pol