A070514 Final digit of n^4: a(n) = n^4 mod 10.

0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0, 1, 6, 1, 6, 5, 6, 1, 6, 1, 0

Offset

0,3

Comments

Decimal expansion of 538853870/3333333333. - Alexander R. Povolotsky, Mar 09 2013

Links

Table of n, a(n) for n=0..100.

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

Formula

a(n) = n^k mod 10; for k > 0 where k mod 4 = 0. - Doug Bell, Jun 15 2015

From G. C. Greubel, Apr 01 2016: (Start)

a(n) = a(n-10).

a(2*n) = 6*A011558(n).

G.f.: (x +6*x^2 +x^3 +6*x^4 +5*x^5 +6*x^6 +x^7 +6*x^8 +x^9)/(1 - x^10). (End)

Maple

A070514:=n->n^4 mod 10: seq(A070514(n), n=0..100); # Wesley Ivan Hurt, Apr 01 2016

Mathematica

LinearRecurrence[{0, 0, 0, 0, 0, 0, 0, 0, 0, 1}, {0, 1, 6, 1, 6, 5, 6, 1, 6, 1}, 100] (* Vincenzo Librandi, Jun 16 2015 *)
PowerMod[Range[0, 100], 4, 10] (* G. C. Greubel, Apr 01 2016 *)

Prog

(Sage) [power_mod(n, 4, 10)for n in range(0, 101)] # Zerinvary Lajos, Oct 30 2009
(Magma) [n^4 mod (10): n in [0..80]]; // Vincenzo Librandi, Jun 16 2015
(PARI) vector(100, n, n--; n^4%10) \\ Derek Orr, Jun 16 2015

Crossrefs

Cf. A010879, A008959, A008960. - Doug Bell, Jun 15 2015

Sequence in context: A010492 A276515 A144544 * A169886 A292862 A070472

Adjacent sequences: A070511 A070512 A070513 * A070515 A070516 A070517

Keyword

nonn,base

Author

N. J. A. Sloane, May 13 2002

Status

approved