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A217538
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Integer part of the n-th partial sum of the reciprocal primes gaps.
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4
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1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 19, 20, 20, 20, 20, 20, 20, 21, 21, 21, 21, 21, 21, 22, 22, 22, 23
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OFFSET
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1,3
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COMMENTS
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Integer part of 1, 3/2, 2, 9/4, 11/4, 3, 7/2, 15/4, 47/12, 53/12, 55/12, 29/6...
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LINKS
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FORMULA
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a(n) = floor(Sum_{i=1..n} 1/A001223(i) ).
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EXAMPLE
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For n = 2 we have the first two prime gaps: 3-2=1 and 5-3=2, then the sum of the reciprocals is 1/1 + 1/2 = 3/2 and its integer part is 1, then a(2) = 1.
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MAPLE
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floor(%) ;
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MATHEMATICA
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Table[Floor@Sum[1/(Prime[j + 1] - Prime[j]), {j, 1, n}], {n, 1, 64}]
Floor[Accumulate[1/Differences[Prime[Range[90]]]]] (* Harvey P. Dale, May 10 2021 *)
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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