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A062020
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a(n) = Sum_{i=1..n} Sum_{j=1..i} (prime(i) - prime(j)).
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6
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0, 1, 6, 17, 44, 81, 142, 217, 324, 485, 666, 913, 1208, 1529, 1906, 2373, 2936, 3533, 4238, 5019, 5840, 6787, 7822, 8995, 10360, 11825, 13342, 14967, 16648, 18445, 20662, 23003, 25536, 28135, 31074, 34083, 37308, 40755, 44354, 48187, 52260
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OFFSET
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1,3
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LINKS
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FORMULA
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a(n) = a(n-1) + n*prime(n) - Sum_{i = 1..n} prime(i), with a(0) = 0.
a(n) = 2*a(n-1) - a(n-2) + (n-1)*(prime(n) - prime(n-1)), with a(1) = 0, a(2) = 1.
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EXAMPLE
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a(3) = (5-2) + (5-3) + (3-2) = 6.
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MATHEMATICA
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a[n_]:= a[n]= If[n<3, (n-1), 2*a[n-1] -a[n-2] +(n-1)*(Prime[n] -Prime[n-1])];
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PROG
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(SageMath)
@CachedFunction
if (n<3): return (n-1)
else: return 2*a(n-1) - a(n-2) + (n-1)*(nth_prime(n) - nth_prime(n-1))
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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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More terms from Larry Reeves (larryr(AT)acm.org), Jun 05 2001
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STATUS
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approved
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