A201644 The first of the five known sets of nine distinct odd numbers the sum of whose reciprocals is 1.

3, 5, 7, 9, 11, 15, 35, 45, 231

Offset

1,1

Comments

John Leech showed that nine is the smallest number of odd numbers with this property.

This set was apparently discovered by S. Yamashita in 1976.

References

R. K. Guy, Unsolved Problems in Number Theory (UPINT), Section D11.

Links

Table of n, a(n) for n=1..9.

Nechemia Burshtein, The equation sum(i=1,9,1/xi)=1 in distinct odd integers has only the five known solutions, Journal of Number Theory, Volume 127, Issue 1, November 2007, Pages 136-144.

The Prime Puzzles and Problems Connection, Problem 35

Index entries for sequences related to Egyptian fractions

Example

1/3+1/5+1/7+1/9+1/11+1/15+1/35+1/45+1/231 = 1.

Crossrefs

There are five known sets of nine odd numbers with this property: A201644, A201646, A201647, A201648, A201649.

Sequence in context: A133848 A220077 A201649 * A342949 A322400 A322553

Adjacent sequences: A201641 A201642 A201643 * A201645 A201646 A201647

Keyword

nonn,fini,full

Author

N. J. A. Sloane, Dec 03 2011

Status

approved