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

0,3

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

Table of n, a(n) for n=0..86.

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).

Formula

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

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 *)

Prog

(Perl) print (($_**$_-$_)%10) for (1..40);
(PARI) a(n)=lift(Mod(n, 10)^n-n) \\ Charles R Greathouse IV, Mar 13 2012

Crossrefs

Cf. A056849.

Sequence in context: A317896 A320364 A318222 * A277659 A331144 A258711

Adjacent sequences: A209463 A209464 A209465 * A209467 A209468 A209469

Keyword

nonn,easy,base

Author

Radu Borza, Mar 09 2012

Status

approved