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A162939
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A 1-based alternate sum over the numbers from 0 to prime(n).
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3
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1, 5, 8, 11, 17, 20, 26, 29, 35, 44, 47, 56, 62, 65, 71, 80, 89, 92, 101, 107, 110, 119, 125, 134, 146, 152, 155, 161, 164, 170, 191, 197, 206, 209, 224, 227, 236, 245, 251, 260, 269, 272, 287, 290, 296, 299, 317, 335, 341, 344, 350, 359, 362, 377, 386, 395, 404
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OFFSET
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1,2
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COMMENTS
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Define a 1-based sum S(n) = sum_{i=1..n} (1 - (-1)^i*i) = A014682(n).
a(n) is this sum evaluated for the upper limit prime(n) = A000040(n).
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LINKS
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EXAMPLE
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a(1) = 1-1*(-1)^1+1-2*(-1)^2 = 1+1+1-2 = 1.
a(3) = 1-1*(-1)^1+1-2*(-1)^2+1-3*(-1)^3+1-4*(-1)^4+1-5*(-1)^5 = 1+1+1-2+1+3+1-4+1+5 = 8.
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MAPLE
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A014682 := proc(n) option remember; coeftayl( x*(2+x+x^2)/(1-x^2)^2, x=0, n) ; end:
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MATHEMATICA
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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