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

Author

N. J. A. Sloane, May 13 2002

Keywords

• nonn
• base

Comments

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

Links

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

Crossrefs

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

Programs

Magma

[n^4 mod (10): n in [0..80]]; // Vincenzo Librandi, Jun 16 2015

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 *)

PARI

vector(100,n,n--;n^4%10) \\ Derek Orr, Jun 16 2015

Sage

[power_mod(n,4,10)for n in range(0, 101)] # Zerinvary Lajos, Oct 30 2009

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)