

A052488


a(n) = floor(n*H(n)) where H(n) is the nth harmonic number, Sum_{k=1..n} 1/k (A001008/A002805).


6



1, 3, 5, 8, 11, 14, 18, 21, 25, 29, 33, 37, 41, 45, 49, 54, 58, 62, 67, 71, 76, 81, 85, 90, 95, 100, 105, 109, 114, 119, 124, 129, 134, 140, 145, 150, 155, 160, 165, 171, 176, 181, 187, 192, 197, 203, 208, 214, 219, 224, 230, 235, 241, 247, 252, 258, 263, 269
(list;
graph;
refs;
listen;
history;
text;
internal format)



OFFSET

1,2


COMMENTS

Floor(n*H(n)) gives a (very) rough approximation to the nth prime.
a(n) is the integer part of the solution to the Coupon Collector's Problem. For example, if there are n=4 different prizes to collect from cereal boxes and they are equally likely to be found, then the integer part of the average number of boxes to buy before the collection is complete is a(4)=8.  Ron Lalonde (ronronronlalonde(AT)hotmail.com), Feb 04 2004


REFERENCES

John D. Barrow, One Hundred Essential Things You Didn't Know You Didn't Know, Ch. 3, 'On the Cards', W. W. Norton & Co., NY & London, 2008, pp. 3032.


LINKS

Robert Israel, Table of n, a(n) for n = 1..10000


MAPLE

for n from 1 to 100 do printf(`%d, `, floor(n*sum(1/k, k=1..n))) od:
# Alternatively:
A052488:= n > floor(n*(Psi(n+1)+gamma));
seq(A052488(n), n=1..100); # Robert Israel, May 19 2014


MATHEMATICA

f[n_] := Floor[n*HarmonicNumber[n]]; Array[f, 60] (* Robert G. Wilson v, Nov 23 2015 *)


PROG

(PARI) a(n) = floor(n*sum(k=1, n, 1/k)) \\ Altug Alkan, Nov 23 2015
(MAGMA) [Floor(n*HarmonicNumber(n)): n in [1..60]]; // G. C. Greubel, May 14 2019
(Sage) [floor(n*harmonic_number(n)) for n in (1..60)] # G. C. Greubel, May 14 2019


CROSSREFS

Cf. A001008, A002805, A006218, A060293.
Cf. A001620, A073004.
Sequence in context: A310027 A310028 A287414 * A076372 A248611 A005356
Adjacent sequences: A052485 A052486 A052487 * A052489 A052490 A052491


KEYWORD

easy,nonn


AUTHOR

Tomas Mario Kalmar (TomKalmar(AT)aol.com), Mar 15 2000


EXTENSIONS

More terms from James A. Sellers, Mar 17 2000


STATUS

approved



