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A081881 Pack bins of size 1 sequentially with items of size 1/1, 1/2, 1/3, 1/4, ... . Sequence gives values of n for which 1/n starts a new bin. 5
1, 2, 4, 10, 26, 69, 186, 504, 1369, 3720, 10111, 27483, 74705, 203068, 551995, 1500477, 4078718, 11087104, 30137872, 81923228, 222690421, 605335323, 1645472007, 4472856655, 12158484965 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Needs a b-file. - N. J. A. Sloane, Nov 30 2017

For n >= 3, it appears that a(n) = round((a(n-1) - 1/2)*e). Verified through n = 10000 (using the approximation Sum_{j=1..k} 1/j = log(k) + gamma + 1/(2*k) - 1/(12*k^2) + 1/(120*k^4) - 1/(252*k^6) + 1/(240*k^8) - ... + 7709321041217/(16320*k^32), where gamma is the Euler-Mascheroni constant, A001620). - Jon E. Schoenfield, Mar 30 2018

LINKS

Table of n, a(n) for n=1..25.

FORMULA

a(n) is asymptotic to C*exp(n) where C=0.1688... - Benoit Cloitre, Apr 14 2003

C = 0.16885635666714420373167977550090103410150395689764... (cf. A300897). - Jon E. Schoenfield, Apr 12 2018

a(n) = 1 + (A136616^(n-1))(0). - Rainer Rosenthal, Feb 16 2008

EXAMPLE

1/1; 1/2+1/3, 1/4+1/5+1/6+1/7+1/8+1/9 are all just less than or equal to 1; so first four terms are 1, 2, 4, 10.

Lower and upper indices of bin contents are {1,1}, {2,3}, {4,9}, {10,25}, {26,68}, {69,185}, {186,503}, {504,1368}, {1369,3719}, {3720,10110}, {10111,27482}, ...

MATHEMATICA

res ={}; FoldList[If[ #1+#2 > 1, AppendTo[res, #2]; #2, #1+#2]&, 0, Table[1/k, {k, 1, 1000}]]; 1/res

lst = {1, 2}; n = 2; Do[s = 0; While[s = N[s + 1/n, 64]; s < 1, n++ ]; AppendTo[lst, n]; Print@n, {i, 25}]; lst (* Robert G. Wilson v, Aug 19 2008 *)

CROSSREFS

Cf. A002387, A136616, A136617, A300897.

Sequence in context: A052995 A113337 A084575 * A025565 A085455 A055226

Adjacent sequences:  A081878 A081879 A081880 * A081882 A081883 A081884

KEYWORD

nonn,nice

AUTHOR

Wouter Meeussen, Apr 13 2003

EXTENSIONS

a(13)-a(25) from Robert G. Wilson v, Aug 19 2008

STATUS

approved

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Last modified April 24 18:03 EDT 2019. Contains 322430 sequences. (Running on oeis4.)