A240775 The six values n in each interval [i*840, (i+1)*840), where i >= 0, for which Mordell's formulas do NOT provide a three-Egyptian-fraction solution for 4/n.

1, 121, 169, 289, 361, 529

Offset

1,2

Comments

Erdős and Straus conjectured that for all integers n >= 2, the rational number 4/n can be expressed as an Egyptian fraction with exactly three unit fractions -- that is, 4/n = 1/x + 1/y + 1/z where x, y and z are positive integers. The conjecture has been verified to high values of n, and Mordell has provided formulas to compute x, y and z for many n. The values of n NOT included in Mordell's formulas are those for which n modulo 840 = {an element of this sequence}. Each element is the square of a prime.

References

Louis J. Mordell, Diophantine Equations, Academic Press, 1967, 287-290.

Links

Table of n, a(n) for n=1..6.

Formula

a(1)=1^2, a(2)=11^2, a(3)=13^2, a(4)=17^2, a(5)=19^2, a(6)=23^2. - Andrés Ventas, May 25 2026

Crossrefs

Cf. A139665

Sequence in context: A258693 A037266 A352221 * A346316 A284643 A074730

Adjacent sequences: A240772 A240773 A240774 * A240776 A240777 A240778

Keyword

nonn,fini,full

Author

Kenneth Vollmar, Apr 12 2014

Status

approved