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 A237684 a(n) = floor(n*prime(n) / Sum_{i<=n} prime(i). 1

%I

%S 1,1,1,1,1,1,2,1,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,

%T 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,

%U 2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2,2

%N a(n) = floor(n*prime(n) / Sum_{i<=n} prime(i).

%C a(n) = 1 for n = 8 and 1 <= n <=6.

%C a(n) = 2 for n = 7 and 9 <= n < 10^11 (verified terms).

%C Conjectures:

%C (1): a(n) = 1 or 2 for all n.

%C (2): sequence of numbers n sorted by decreasing values of function f(n) = n*Prime(n) / Sum_i<=n (Prime(i): 48, 35, 31, 25, 17, 49, 33, 69, 32, 26, 43, 38, 12, 63, 102, 67, 68, 37, … The last term of this sequence is 1.

%C (3): maximal value of function f(n) is for n = 48: f(48) = 10704/4661 = 2.29650289637416...

%C (4): minimal value of function f(n) is for n = 1: f(1) = 1.

%H Jaroslav Krizek, <a href="/A237684/b237684.txt">Table of n, a(n) for n = 1..87</a>

%F a(n) = floor(A033286(n) / A007504(n)).

%e For n=8: a(8) = floor(8*Prime(8) / Sum_i<=8 (Prime(i)) = 8*19 / 77 = 1.

%K nonn

%O 1,7

%A _Jaroslav Krizek_, Feb 21 2014

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Last modified December 1 09:28 EST 2020. Contains 338833 sequences. (Running on oeis4.)