A209466 Final digit of n^n - n.

1, 0, 2, 4, 2, 0, 0, 6, 8, 0, 0, 0, 4, 0, 2, 0, 0, 0, 6, 0, 0, 0, 2, 4, 2, 0, 0, 6, 8, 0, 0, 0, 4, 0, 2, 0, 0, 0, 6, 0, 0, 0, 2, 4, 2, 0, 0, 6, 8, 0, 0, 0, 4, 0, 2, 0, 0, 0, 6, 0, 0, 0, 2, 4, 2, 0, 0, 6, 8, 0, 0, 0, 4, 0, 2, 0, 0, 0, 6, 0, 0, 0, 2, 4, 2, 0, 0

Offset: 0

Author

Radu Borza, Mar 09 2012

Keywords

• nonn
• easy
• base

Comments

Note: cyclic with a period of 20 for n > 0.

References

• R. Euler & J. Sadek, "A number that gives the units of n^n", Journal of Recreational Mathematics 29:3 (1998), pp. 203-204.

Links

• Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Crossrefs

Cf. A056849.

Programs

Maple

[seq((n^n-n) mod 10, n=1..40)];

Mathematica

Join[{1}, Table[Mod[PowerMod[n, n, 10] - n, 10], {n, 100}]] (* T. D. Noe, Mar 13 2012 *)
PadRight[{1},120,{0,0,2,4,2,0,0,6,8,0,0,0,4,0,2,0,0,0,6,0}] (* Harvey P. Dale, May 21 2020 *)

PARI

a(n)=lift(Mod(n,10)^n-n) \\ Charles R Greathouse IV, Mar 13 2012

Perl

print (($**$-$_)%10) for (1..40);

Formula

a(n) = (n^n-n) mod 10