

A070653


a(n) = n^6 mod 30.


0



0, 1, 4, 9, 16, 25, 6, 19, 4, 21, 10, 1, 24, 19, 16, 15, 16, 19, 24, 1, 10, 21, 4, 19, 6, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 6, 19, 4, 21, 10, 1, 24, 19, 16, 15, 16, 19, 24, 1, 10, 21, 4, 19, 6, 25, 16, 9, 4, 1, 0, 1, 4, 9, 16, 25, 6, 19, 4, 21, 10, 1, 24, 19, 16, 15, 16, 19, 24, 1
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OFFSET

0,3


COMMENTS

a(n) = A070452(n). [Proof: n^6  n^2 == 0 (mod 30) is shown explicitly for n=0 to 29, then the induction n>n+30 for the 6thorder polynomial followed by binomial expansion of (n+30)^k concludes that the zero (mod 30) is periodically extended to the other integers.]  R. J. Mathar, Jul 23 2009


LINKS

Table of n, a(n) for n=0..79.


MATHEMATICA

Table[Mod[n^6, 30], {n, 0, 200}] (* Vladimir Joseph Stephan Orlovsky, Apr 27 2011 *)


PROG

(Sage) [power_mod(n, 6, 30)for n in range(0, 75)] # Zerinvary Lajos, Nov 03 2009
(PARI) a(n)=n^6%30 \\ Charles R Greathouse IV, Apr 06 2016


CROSSREFS

Cf. A070450, A070451, A070452.
Sequence in context: A070454 A070453 A070452 * A304233 A070451 A070450
Adjacent sequences: A070650 A070651 A070652 * A070654 A070655 A070656


KEYWORD

nonn,easy


AUTHOR

N. J. A. Sloane, May 13 2002


STATUS

approved



