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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; internal format)
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OFFSET
| 0,3
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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.] [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 23 2009]
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FORMULA
| 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) ). - R. J. Mathar, Mar 14 2011
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MATHEMATICA
| Table[Mod[n^6, 15], {n, 0, 200}] (* From Vladimir Joseph Stephan Orlovsky, Apr 21 2011 *)
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PROG
| (Other) sage: [power_mod(n, 6, 15)for n in xrange(0, 97)] # [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Nov 06 2009]
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CROSSREFS
| Cf. A070437, A070438.
Sequence in context: A197266 A200393 A070438 * A152205 A129861 A055491
Adjacent sequences: A070635 A070636 A070637 * A070639 A070640 A070641
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com), May 13 2002
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