Search: id:a047217
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A047217
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Numbers that are congruent to {0, 1, 2} mod 5.
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+0
25
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0, 1, 2, 5, 6, 7, 10, 11, 12, 15, 16, 17, 20, 21, 22, 25, 26, 27, 30, 31, 32, 35, 36, 37, 40, 41, 42, 45, 46, 47, 50, 51, 52, 55, 56, 57, 60, 61, 62, 65, 66, 67, 70, 71, 72, 75, 76, 77, 80, 81, 82, 85, 86, 87, 90, 91, 92, 95, 96, 97, 100, 101, 102, 105, 106, 107, 110, 111
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OFFSET
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1,3
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COMMENTS
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Also, the only numbers that are eligible to be the sum of two 4th powers (A004831). - Cino Hilliard, Nov 23 2003
Nonnegative m such that floor(2*m/5) = 2*floor(m/5). - Bruno Berselli, Dec 09 2015
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LINKS
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FORMULA
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G.f.: x^2*(1+x+3*x^2)/(1-x)^2/(1+x+x^2). - Colin Barker, Feb 17 2012
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(n) = (15*n-21-6*cos(2*n*Pi/3)+2*sqrt(3)*sin(2*n*Pi/3))/9.
a(3*k) = 5*k-3, a(3*k-1) = 5*k-4, a(3*k-2) = 5*k-5. (End)
Sum_{n>=2} (-1)^n/a(n) = sqrt(1-2/sqrt(5))*Pi/5 + 3*log(2)/5. - Amiram Eldar, Dec 10 2021
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MAPLE
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seq(op([5*i, 5*i+1, 5*i+2]), i=0..100); # Robert Israel, Sep 02 2014
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MATHEMATICA
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Select[Range[0, 120], MemberQ[{0, 1, 2}, Mod[#, 5]]&] (* Harvey P. Dale, Jan 20 2012 *)
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PROG
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(PARI) concat(0, Vec(x^2*(1+x+3*x^2)/(1-x)^2/(1+x+x^2) + O(x^100))) \\ Altug Alkan, Dec 09 2015
(Magma) I:=[0, 1, 2, 5]; [n le 4 select I[n] else Self(n-1)+Self(n-3)-Self(n-4): n in [1..70]]: // Vincenzo Librandi, Apr 25 2012
(Magma) &cat [[5*n, 5*n+1, 5*n+2]: n in [0..30]]; // Bruno Berselli, Dec 09 2015
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CROSSREFS
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Cf. similar sequences with formula n+i*floor(n/3) listed in A281899.
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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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