A217538 - OEIS

%I #45 May 10 2021 11:00:17

%S 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,

%T 10,11,11,11,11,12,12,12,12,13,13,14,14,14,14,15,15,15,15,16,16,16,16,

%U 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

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

%C Integer part of 1, 3/2, 2, 9/4, 11/4, 3, 7/2, 15/4, 47/12, 53/12, 55/12, 29/6...

%H Harvey P. Dale, <a href="/A217538/b217538.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = floor(Sum_{i=1..n} 1/A001223(i) ).

%e 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.

%p A217538 := proc(n)

%p         add(1/A001223(i),i=1..n) ;

%p         floor(%) ;

%p end proc: # _R. J. Mathar_, Jun 26 2016

%t Table[Floor@Sum[1/(Prime[j + 1] - Prime[j]), {j, 1, n}], {n, 1, 64}]

%t Floor[Accumulate[1/Differences[Prime[Range[90]]]]] (* _Harvey P. Dale_, May 10 2021 *)

%Y Cf. A001223.

%K nonn

%O 1,3

%A _Andres Cicuttin_, Jun 23 2016