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a(n) = floor(Sum_{k=1..n} 0.k).
1

%I #8 Sep 08 2022 08:46:17

%S 0,0,0,1,1,2,2,3,4,4,4,4,4,5,5,5,5,5,5,6,6,6,6,7,7,7,7,8,8,8,9,9,9,10,

%T 10,10,11,11,11,12,12,13,13,13,14,14,15,15,16,16,17,17,18,18,19,20,20,

%U 21,21,22,22,23,24,24,25,26,26,27,28,28,29,30,31

%N a(n) = floor(Sum_{k=1..n} 0.k).

%C Here 0.k means the decimal fraction obtained by writing k after the decimal point, e.g. 0.12 = 12/100 = 3/25.

%C The first few values of Sum_{k=1..n} 0.k are: 1/10, 3/10, 3/5, 1, 3/2, 21/10, 14/5, 18/5, 9/2, 23/5, ...

%C Conjecture: function ((Sum_{k=1..n} 0.k) / n) is bounded above by values 0.55.

%H Jaroslav Krizek, <a href="/A276646/b276646.txt">Table of n, a(n) for n = 1..1000</a>

%F a(n) = floor(A275625(n)/A275626(n)).

%e For n=12; a(12) = floor(Sum_{k=1..12} 0.k) = floor(0.1 + 0.2 + 0.3 + 0.4 + 0.5 + 0.6 + 0.7 + 0.8 + 0.9 + 0.10 + 0.11 + 0.12 = 4.83) = floor(483/100) = 4.

%o (Magma) [Floor(&+[k / (10^(#Intseq(k))): k in [1..n]]): n in [1..1000]]

%Y Cf. A054464, A275625, A275626, A275623, A275624.

%K nonn

%O 1,6

%A _Jaroslav Krizek_, Sep 09 2016