login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

a(n) is the largest k such that the sum of k consecutive reciprocals 1/p_n + ... + 1/p_(n+k-1) does not exceed 1 (where p_n = n-th prime).
0

%I #19 Sep 29 2019 11:34:54

%S 2,8,26,65,143,252,423,650,976,1391,1865,2478,3168,3980,4977,6136,

%T 7419,8828,10476,12278,14294,16612,19123,21905,24903,28055,31493,

%U 35319,39485,44101,49115,54102,59467,65142,71314,77648,84503,91719,99302,107364

%N a(n) is the largest k such that the sum of k consecutive reciprocals 1/p_n + ... + 1/p_(n+k-1) does not exceed 1 (where p_n = n-th prime).

%C The sequence is nondecreasing, since 1/p_n + ... + 1/p_(n+k-1) > 1/p_(n+1) + ... + 1/p_(n+k).

%F a(n) = A137368(n) - 1.

%e For n = 1, since 1/p_1 + 1/p_2 = 1/2 + 1/3 = 5/6 <= 1 while 1/p_1 + 1/p_2 + 1/p_3 = 1/2 + 1/3 + 1/5 = 31/30 > 1, a(1) = 2.

%Y Analog of A136617. Cf. A137368.

%K nonn

%O 1,1

%A _Leon Bykov_, Sep 18 2019