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A146763
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Rank of terms ending in 0 in A061039.
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2
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0, 4, 10, 14, 20, 24, 30, 34, 40, 44, 50, 54, 60, 64, 70, 74, 80, 84, 90, 94, 100, 104, 110, 114, 120, 124, 130, 134, 140, 144, 150, 154, 160, 164, 170, 174, 180, 184, 190, 194, 200, 204, 210, 214, 220, 224, 230, 234, 240, 244, 250, 254, 260, 264, 270, 274
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OFFSET
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0,2
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COMMENTS
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From Paschen spectrum of hydrogen.
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LINKS
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FORMULA
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a(n) = (-1 + (-1)^n + 10*n)/2.
a(n) = a(n-1) + a(n-2) - a(n-3).
G.f.: x*(4+6*x)/((1-x)^2*(1+x)). (End)
E.g.f.: 1/2 (exp(-x) - (1 - 10*x)*exp(x)). - G. C. Greubel, Mar 10 2022
Sum_{n>=1} (-1)^(n+1)/a(n) = sqrt(1-2/sqrt(5))*Pi/20 - log(phi)/(4*sqrt(5)) + log(5)/8, where phi is the golden ratio (A001622). - Amiram Eldar, Sep 17 2023
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MATHEMATICA
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Select[Range[0, 100], MemberQ[{0, 4}, Mod[#, 10]] &] (* K G Teal, Dec 02 2014 *)
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PROG
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(Magma) [5*n - (n mod 2): n in [0..60]]; // G. C. Greubel, Mar 10 2022
(Sage) [5*n - (n%2) for n in (0..60)] # G. C. Greubel, Mar 10 2022
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CROSSREFS
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KEYWORD
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nonn,base,easy
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AUTHOR
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STATUS
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approved
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