A071358 Least k>0 such that the last digit of (n+k)^n is the same as the last digit of n^n.

10, 6, 10, 2, 10, 8, 10, 4, 10, 10, 10, 2, 10, 2, 10, 2, 10, 4, 10, 10, 10, 6, 10, 2, 10, 8, 10, 4, 10, 10, 10, 2, 10, 2, 10, 2, 10, 4, 10, 10, 10, 6, 10, 2, 10, 8, 10, 4, 10, 10, 10, 2, 10, 2, 10, 2, 10, 4, 10, 10, 10, 6, 10, 2, 10, 8, 10, 4, 10, 10, 10, 2, 10, 2, 10, 2, 10, 4, 10, 10

Offset

1,1

Links

Table of n, a(n) for n=1..80.

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) is periodic with period (10, 6, 10, 2, 10, 8, 10, 4, 10, 10, 10, 2, 10, 2, 10, 2, 10, 4, 10, 10) of length 20

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {10, 6, 10, 2, 10, 8, 10, 4, 10, 10, 10, 2, 10, 2, 10, 2, 10, 4, 10, 10}, 80] (* Ray Chandler, Aug 26 2015 *)

Prog

(PARI) a(n)=if(n<0, 0, s=1; while(abs((n+s)^n%10-n^n%10)>0, s++); s)
(Python)
def a(n):
    k, target = 2, pow(n, n, 10)
    while pow(n+k, n, 10) != target: k += 2
    return k
print([a(n) for n in range(1, 81)]) # Michael S. Branicky, Oct 06 2021

Crossrefs

Sequence in context: A304879 A105155 A072930 * A167873 A369702 A033986

Adjacent sequences: A071355 A071356 A071357 * A071359 A071360 A071361

Keyword

easy,nonn,base

Author

Benoit Cloitre, Aug 13 2002

Status

approved