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A046633
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Number of cubic residues mod 5^n.
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3
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1, 5, 21, 101, 505, 2521, 12601, 63005, 315021, 1575101, 7875505, 39377521, 196887601, 984438005, 4922190021, 24610950101, 123054750505, 615273752521, 3076368762601, 15381843813005, 76909219065021, 384546095325101
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OFFSET
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0,2
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LINKS
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FORMULA
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a(n) = A046530(5^n). Conjecture: a(n)= +5*a(n-1) +a(n-3) -5*a(n-4) with g.f. ( 1-4*x^2-5*x^3 ) / ( (x-1)*(5*x-1)*(1+x+x^2) ). - R. J. Mathar, Feb 27 2011
31*a(n) = 5^(n+2)+2*b(n), where b(n)=3 if n==0 (mod 3), b(n)=15 if n==1 (mod 3) and b(n)=13 if b(n)==2 (mod 3). - R. J. Mathar, Oct 08 2017
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MAPLE
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5^(n+2)+2*op(1+modp(n, 3), [3, 15, 13]) ;
%/31 ;
end proc:
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MATHEMATICA
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a[n_] := a[n] = Table[PowerMod[k, 3, 5^n], {k, 1, 5^n}] // Union // Length;
Table[Print["a(", n, ") = ", a[n]]; a[n], {n, 0, 10}]
(* or: *)
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PROG
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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