A167873 Period 4: repeat [10, 6, 10, 4].

10, 6, 10, 4, 10, 6, 10, 4, 10, 6, 10, 4, 10, 6, 10, 4, 10, 6, 10, 4, 10, 6, 10, 4, 10, 6, 10, 4, 10, 6, 10, 4, 10, 6, 10, 4, 10, 6, 10, 4, 10, 6, 10, 4, 10, 6, 10, 4, 10, 6, 10, 4, 10, 6, 10, 4, 10, 6, 10, 4, 10, 6, 10, 4, 10, 6, 10, 4, 10, 6, 10, 4

Offset

1,1

Comments

Number of different remainders mod 10 of n-th powers (i.e., number of possible last decimal digits of n-th powers).

Continued fraction expansion of (124+sqrt(16926))/25. - Klaus Brockhaus, May 01 2010

Links

Muniru A Asiru, Table of n, a(n) for n = 1..1000

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

Formula

a(n) = 8 - 4*((n+1) mod 2) + 2*ceiling(n/4) - 2*floor(n/4). - Wesley Ivan Hurt, Mar 26 2014

a(n) = 15/2 - (5/2)*cos(n*Pi) - cos(n*Pi/2). - Wesley Ivan Hurt, Oct 05 2018

Example

a(4) = 4 because the possible last decimal digits of 4th powers are 0, 1, 5, 6.

Maple

seq(op([10, 6, 10, 4]), n=0..30); # Wesley Ivan Hurt, Oct 06 2018

Mathematica

PadRight[{}, 80, {10, 6, 10, 4}] (* Harvey P. Dale, Nov 29 2015 *)

Prog

(GAP) Flat(List([1..30], n->[10, 6, 10, 4])); # Muniru A Asiru, Oct 06 2018

Crossrefs

Cf. A177015 (decimal expansion of (124+sqrt(16926))/25). - Klaus Brockhaus, May 01 2010

Sequence in context: A105155 A072930 A071358 * A369702 A033986 A049004

Adjacent sequences: A167870 A167871 A167872 * A167874 A167875 A167876

Keyword

easy,nonn

Author

Franz Vrabec, Nov 14 2009

Status

approved