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A084967
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Multiples of 5 whose GCD with 6 is 1.
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26
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5, 25, 35, 55, 65, 85, 95, 115, 125, 145, 155, 175, 185, 205, 215, 235, 245, 265, 275, 295, 305, 325, 335, 355, 365, 385, 395, 415, 425, 445, 455, 475, 485, 505, 515, 535, 545, 565, 575, 595, 605, 625, 635, 655, 665, 685, 695, 715, 725, 745, 755, 775, 785
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OFFSET
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1,1
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COMMENTS
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LINKS
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FORMULA
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Numbers of the form 5k for which gcd(5k, 6) = 1.
a(n) = 5*(-3 + (-1)^n + 6*n)/2.
a(n) = a(n-1) + a(n-2) - a(n-3).
G.f.: 5*x*(x^2+4*x+1) / ((x-1)^2*(x+1)). (End)
For n > 2, a(n) = a(n-2) + 30. - Zak Seidov, Apr 29 2015
Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/(10*sqrt(3)). - Amiram Eldar, Nov 03 2022
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MATHEMATICA
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5Select[ Range[160], GCD[ #, 2*3] == 1 & ]
Select[Range[5, 785, 10], Mod[#, 3] > 0 &] (* Zak Seidov, Apr 29 2015 *)
a[1] = 5; a[n_] := a[n] = a[n - 1] + 10*(2 - Mod[n, 2]); Table[a[n], {n, 50}] (* Zak Seidov, Apr 29 2015 *)
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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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