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A070638 a(n) = n^6 mod 15. 0
0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6, 4, 4, 6, 10, 1, 9, 4, 1, 0, 1, 4, 9, 1, 10, 6 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

a(n) = A070438(n). [Proof: n^6 - n^2 == 0 (mod 15) is shown explicitly for n=0 to 14, then the induction n->n+15 for the 6th-order polynomial followed by binomial expansion of (n+15)^k concludes that the zero (mod 15) is periodically extended to the other integers.] - R. J. Mathar, Jul 23 2009

LINKS

Table of n, a(n) for n=0..96.

FORMULA

From R. J. Mathar, Mar 14 2011: (Start)

a(n) = a(n-15).

G.f.: -x*(1+x) *(x^12+3*x^11+6*x^10-5*x^9+15*x^8-9*x^7+13*x^6-9*x^5+15*x^4-5*x^3+6*x^2+3*x+1) / ( (x-1) *(1+x^4+x^3+x^2+x) *(1+x+x^2) *(1-x+x^3-x^4+x^5-x^7+x^8) ). (End)

MATHEMATICA

Table[Mod[n^6, 15], {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Apr 21 2011 *)

PROG

(Sage) [power_mod(n, 6, 15)for n in range(0, 97)] # - Zerinvary Lajos, Nov 06 2009

(PARI) a(n)=n^6%15 \\ Charles R Greathouse IV, Apr 06 2016

CROSSREFS

Cf. A070437, A070438.

Sequence in context: A197266 A200393 A070438 * A236104 A152205 A129861

Adjacent sequences:  A070635 A070636 A070637 * A070639 A070640 A070641

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, May 13 2002

STATUS

approved

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Last modified May 6 00:41 EDT 2021. Contains 343579 sequences. (Running on oeis4.)