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A217538
Integer part of the n-th partial sum of the reciprocal primes gaps.
4
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
OFFSET
1,3
COMMENTS
Integer part of 1, 3/2, 2, 9/4, 11/4, 3, 7/2, 15/4, 47/12, 53/12, 55/12, 29/6...
LINKS
FORMULA
a(n) = floor(Sum_{i=1..n} 1/A001223(i) ).
EXAMPLE
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.
MAPLE
A217538 := proc(n)
add(1/A001223(i), i=1..n) ;
floor(%) ;
end proc: # R. J. Mathar, Jun 26 2016
MATHEMATICA
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 *)
CROSSREFS
Cf. A001223.
Sequence in context: A285189 A051889 A086707 * A333348 A194920 A327440
KEYWORD
nonn
AUTHOR
Andres Cicuttin, Jun 23 2016
STATUS
approved