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A008854
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Numbers that are congruent to {0, 1, 4} mod 5.
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21
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0, 1, 4, 5, 6, 9, 10, 11, 14, 15, 16, 19, 20, 21, 24, 25, 26, 29, 30, 31, 34, 35, 36, 39, 40, 41, 44, 45, 46, 49, 50, 51, 54, 55, 56, 59, 60, 61, 64, 65, 66, 69, 70, 71, 74, 75, 76, 79, 80, 81, 84, 85, 86, 89, 90, 91, 94, 95, 96, 99, 100, 101, 104, 105, 106, 109
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| n^3 and n have same last digit.
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REFERENCES
| L. E. Dickson, History of the Theory of Numbers. Carnegie Institute Public. 256, Washington, DC, Vol. 1, 1919; Vol. 2, 1920; Vol. 3, 1923, see vol. 1, p. 459.
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LINKS
| Index to sequences with linear recurrences with constant coefficients, signature (1,0,1,-1)
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FORMULA
| Partial sums of (0, 1, 3, 1, 1, 3, 1, 1, 3, 1,...). - Gary W. Adamson (qntmpkt(AT)yahoo.com), Jun 19 2008
Contribution from Paolo P. Lava (paoloplava(AT)gmail.com), Sep 03 2010: (Start)
a(n)=-1+Sum_{k=1..n}{(1/9)*[(-k mod 3)+5*((k+1) mod 3)+11*((k+2) mod 3)}, with n>=1
(End)
G.f. x^2*(1+3*x+x^2) / ( (1+x+x^2)*(x-1)^2 ). - R. J. Mathar, Oct 08 2011
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MAPLE
| for n to 1000 do if n^3 - n mod 10 = 0 then print(n); fi; od;
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MATHEMATICA
| Select[Range[0, 150], MemberQ[{0, 1, 4}, Mod[#, 5]]&] (* or *) t={0, 1, 4}; Table[AppendTo[t, t[[n]]+t[[n+1]]]; AppendTo[t, t[[n]]+t[[n+2]]], {n, 2, 45}]; t (* or *) LinearRecurrence[{1, 0, 1, -1}, {0, 1, 4, 5}, 91] (* From Vladimir Joseph Stephan Orlovsky, Jan 21 2012 *)
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CROSSREFS
| Sequence in context: A029776 A177103 A114454 * A062726 A159629 A082812
Adjacent sequences: A008851 A008852 A008853 * A008855 A008856 A008857
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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