Definition:Smith Brothers

Definition

Smith brothers are two consecutive integers which are both Smith numbers.

Sequence of Smith Brothers

The sequence of pairs of Smith brothers begins:

$\tuple {728, 729}, \tuple {2964, 2965}, \tuple {3864, 3865}, \tuple {4959, 4960}, \ldots$

Examples of Smith Brothers

$728$ and $729$

$728$ and $729$ are Smith brothers:

\(\ds 728\)

\(\)

\(\, \ds = \, \)

\(\ds 2^3 \times 7 \times 13\)

\(\ds 7 + 2 + 8\)

\(=\)

\(\, \ds 17 \, \)

\(\, \ds = \, \)

\(\ds 2 + 2 + 2 + 7 + 1 + 3\)

\(\ds 729\)

\(\)

\(\, \ds = \, \)

\(\ds 3^6\)

\(\ds 7 + 2 + 9\)

\(=\)

\(\, \ds 18 \, \)

\(\, \ds = \, \)

\(\ds 3 + 3 + 3 + 3 + 3 + 3\)

Sources

• Weisstein, Eric W. "Smith Brothers." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/SmithBrothers.html