cp's OEIS Frontend

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.

These numbers are of the form 3^k*2^0 + 3^{k-1}*2^{a_1} + ... + 3^1*2^{a_{k-1}} + 3^0*2^{a_k} in which every power 3^i appears, 0 <= i <= k, and where a_i satisfies a_0 = 0, a_0 < a_1 < ... < a_k.

These numbers are of the form 3^k*2^{a_0} + 3^{k-1}*2^{a_1} + ... + 3^1*2^{a_{k-1}} + 3^0*2^{a_k} in which every power 3^i appears, 0 <= i <= k, and where a_i satisfies 0 <= a_0 < a_1 < ... < a_k.

These values are those of sequence A116640 in addition to any multiple of two of elements of this sequence. - Kenneth Vollmar, Jun 05 2013