%I A070597
%S A070597 0,1,8,3,4,5,0,7,8,9,4,11,0,1,8,3,4,5,0,7,8,9,4,11,0,1,8,3,4,5,0,7,8,9,
%T A070597 4,11,0,1,8,3,4,5,0,7,8,9,4,11,0,1,8,3,4,5,0,7,8,9,4,11,0,1,8,3,4,5,0,
%U A070597 7,8,9,4,11,0,1,8,3,4,5,0,7,8,9,4,11,0,1,8,3,4,5,0,7,8,9,4,11,0,1,8,3
%N A070597 n^5 mod 12.
%C A070597 a(n)=A070474(n) [Proof: n^5-n^3 =0 (mod 12) is shown explicitly for n=0 
               to 11, then the induction n->n+12 for the 5th order polynomial followed 
               by binomial expansion of (n+12)^k concludes that the zero (mod 12) 
               is periodically extended to the other integers.] [From R. J. Mathar 
               (mathar(AT)strw.leidenuniv.nl), Jul 23 2009]
%e A070597 Copy sequence SAGE: [0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 
               4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 
               1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 
               11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 
               8, 9, 4, 11, 0, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 0, 1, 8, 3] equal: 
               A070474 [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Oct 
               28 2009]
%o A070597 (Other) sage: [power_mod(n,7,12)for n in xrange(0, 100)] [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Oct 28 2009]
%Y A070597 Sequence in context: A145594 A021849 A070474 this_sequence A091895 A111436 
               A014549
%Y A070597 Adjacent sequences: A070594 A070595 A070596 this_sequence A070598 A070599 
               A070600
%K A070597 nonn
%O A070597 0,3
%A A070597 N. J. A. Sloane (njas(AT)research.att.com), May 13 2002