A157248 'Greedy' sequence formed by summing unit fractions until the sum is 1, and repeating using up the 'left over' fractions.

1, 2, 3, 6, 4, 5, 7, 8, 9, 10, 15, 230, 57960, 11, 12, 13, 14, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 1544, 8242614, 92401258430373, 36895712779713620978746324067

Offset

1,2

Comments

Subsequence of starting elements of each pass may be related to A002387 1,2,4,11,31,83,... - David W. Wilson

References

H. Ibstedt, Computer Analysis of Number Sequences, American Research Press, 1998; Chapter VI.2 Integers represented as sums of terms of the harmonic series.

Links

Jeremy Gardiner, Table of n, a(n) for n=1..94

K. S. Brown's Mathpages, The Greedy Algorithm for Unit Fractions

Example

1/2+1/3+1/6=1

Prog

(PARI) {r=1; u=[]; l=1; for(n=1, 99, while(setsearch(u, l), l++); m=ceil(1/r); while(setsearch(u, m), m++); print1(m", "); r-=1/m; r|r=1; u=setunion(u, Set(m)))} \\ M. F. Hasler

Crossrefs

Cf. A192881.

Sequence in context: A246835 A213625 A132368 * A368229 A085515 A082354

Adjacent sequences: A157245 A157246 A157247 * A157249 A157250 A157251

Keyword

nonn

Author

Jeremy Gardiner, Feb 25 2009

Status

approved