

A238401


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


1



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
(list;
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OFFSET

0,5


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


LINKS

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


FORMULA

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


EXAMPLE

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


PROG

(JavaScript)
c=0;
for (i=1; i<50; i++) {
c+=i/(i+1);
document.write(Math.floor(c)+", ");
}
(PARI) a(n)=nceil(sum(i=2, n, 1./i)) \\ Charles R Greathouse IV, Feb 26 2014


CROSSREFS

Cf. A055980, A001008, A002805.
Sequence in context: A228298 A309082 A124808 * A017862 A265539 A254926
Adjacent sequences: A238398 A238399 A238400 * A238402 A238403 A238404


KEYWORD

nonn


AUTHOR

Jon Perry, Feb 26 2014


EXTENSIONS

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


STATUS

approved



