A238401 Floor(sum(i/(i+1)),i=1..n).

0, 0, 1, 1, 2, 3, 4, 5, 6, 7, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63

Offset: 0

Author

Jon Perry, Feb 26 2014

Keywords

• nonn

Comments

The first numbers which appear twice in the sequence are 0, 1, 7, 26, 77, 220, 608, 1665, 4540, 12356, 33605, 91367, 248383, 675199,... - Giovanni Resta, Feb 26 2014

These numbers appear at roughly exp(n - gamma). - Charles R Greathouse IV, Feb 26 2014

Examples

			a(3) = floor(0/1 + 1/2 + 2/3 + 3/4) = floor(1.91666...) = 1.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A055980, A001008, A002805.

Programs

JavaScript

c=0;
for (i=1;i<50;i++) {
c+=i/(i+1);
document.write(Math.floor(c)+", ");
}

Mathematica

Floor[Accumulate[Table[i/(i+1),{i,0,70}]]] (* Harvey P. Dale, May 18 2023 *)

PARI

a(n)=n-ceil(sum(i=2,n,1./i)) \\ Charles R Greathouse IV, Feb 26 2014

Formula

a(n) = n - log n + O(1). - Charles R Greathouse IV, Feb 26 2014

Extensions

a(50)-a(67) from Giovanni Resta, Feb 26 2014