A217538 Integer part of the n-th partial sum of the reciprocal primes gaps.

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Adjacent sequences: A217535 A217536 A217537 * A217539 A217540 A217541

Keyword

nonn

Author

Andres Cicuttin, Jun 23 2016

Status

approved