A030659 Smallest possible maximum denominator in an expression for 1 as a sum of n distinct unit (Egyptian) fractions.

6, 12, 15, 15, 18, 20, 24, 24, 28, 30, 33, 33, 35, 36, 40, 42, 48, 52, 52, 54, 55, 55, 56, 60, 63, 72, 75, 75, 76, 76, 77, 78, 80, 85, 85, 88, 90, 95, 96, 96, 100, 102, 104, 104, 108, 110, 114, 115, 115, 119, 119, 120, 126, 130, 132, 135, 138, 143, 144, 144

Offset: 3

Author

Dan Hoey

Keywords

• nonn
• hard

References

• R. K. Guy (1981): Unsolved Problems In Number Theory, D11, also p. 161.

Links

• Tatsuru Watanabe, Table of n, a(n) for n = 3..147
• Mohammad K. Azarian, Sylvester's Sequence and the Infinite Egyptian Fraction Decomposition of 1, Problem 958, College Mathematics Journal, Vol. 42, No. 4, September 2011, p. 330. Solution published in Vol. 43, No. 4, September 2012, pp. 340-342.
• David Eppstein, Unit Fractions, smallest last term
• Index entries for sequences related to Egyptian fractions

Crossrefs

Cf. A213062. - Alois P. Heinz, Sep 21 2012

Extensions

More terms from Jon E. Schoenfield, Mar 24 2014