A276646 a(n) = floor(Sum_{k=1..n} 0.k).

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, 10, 10, 11, 11, 11, 12, 12, 13, 13, 13, 14, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 20, 20, 21, 21, 22, 22, 23, 24, 24, 25, 26, 26, 27, 28, 28, 29, 30, 31

Offset

1,6

Comments

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

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, ...

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

Links

Jaroslav Krizek, Table of n, a(n) for n = 1..1000

Formula

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

Example

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.

Prog

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

Crossrefs

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

Sequence in context: A095395 A029134 A303997 * A029130 A081611 A326539

Adjacent sequences: A276643 A276644 A276645 * A276647 A276648 A276649

Keyword

nonn

Author

Jaroslav Krizek, Sep 09 2016

Status

approved