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A209466 Final digit of n^n - n. 0
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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: A011168 A058672 A278215 * A277659 A258711 A127278

Adjacent sequences:  A209463 A209464 A209465 * A209467 A209468 A209469

KEYWORD

nonn,easy,base

AUTHOR

Radu Borza, Mar 09 2012

STATUS

approved

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Last modified February 20 02:07 EST 2018. Contains 299357 sequences. (Running on oeis4.)