A229481 Final digit of 1^n + 2^n + ... + n^n.

0, 1, 5, 6, 4, 5, 1, 4, 2, 5, 5, 6, 0, 1, 5, 0, 8, 3, 9, 0, 6, 1, 5, 6, 0, 5, 1, 4, 8, 5, 5, 6, 6, 1, 5, 0, 4, 3, 9, 0, 2, 1, 5, 6, 6, 5, 1, 4, 4, 5, 5, 6, 2, 1, 5, 0, 0, 3, 9, 0, 8, 1, 5, 6, 2, 5, 1, 4, 0, 5, 5, 6, 8, 1, 5, 0, 6, 3, 9, 0, 4, 1, 5, 6, 8, 5, 1, 4, 6, 5, 5, 6, 4, 1, 5, 0, 2, 3, 9, 0

Offset: 0

Author

José María Grau Ribas, Sep 24 2013

Keywords

• nonn
• base
• easy

Comments

Cyclic with period 100.

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..1000
• 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, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1).

Crossrefs

Cf. A031971, A056849.

Programs

Maple

a:= proc(n) local l; l:=[seq(add(k&^i mod 10, k=1..i) mod 10, i=0..99)]:
      proc(n) l[1+irem(n, 100)] end
    end():
seq(a(n), n=0..200);  # Alois P. Heinz, Sep 26 2013

Mathematica

Table[Mod[Sum[PowerMod[i, n, 10], {i, 1, n}], 10], {n, 0, 133}]

PARI

a(n)=n%=100;lift(sum(k=1,n,Mod(k,10)^n)) \\ Charles R Greathouse IV, Dec 13 2013

Formula

a(n) = a(n-100). - Wesley Ivan Hurt, Jan 02 2024