A201647 The third of the five known sets of nine distinct odd numbers the sum of whose reciprocals is 1.

3, 5, 7, 9, 11, 15, 21, 165, 693

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

Crossrefs

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

Sequence in context: A260124 A376241 A201646 * A201648 A077374 A133848

Adjacent sequences: A201644 A201645 A201646 * A201648 A201649 A201650

Keyword

nonn,fini,full

Author

N. J. A. Sloane, Dec 03 2011

Status

approved