These are numbers    whose representation can be split into two numbers, say    and  , such that the Fibonacci-like sequence which uses    and    as seeds contains    itself.

For example, 549 is a fibodiv since it can be divided into 54 and 9 and they produce the sequence 54, 9, 63, 72, 135, 207, 342, 549,... containing 549 itself.

Note that the 6 fibodiv numbers with 2 digits are, by definition, repfigit numbers, too.

It is easy to see that there are infinite fibodiv numbers, since the numbers 19, 199, 1999,... and 28, 298, 2998,... are all fibodiv numbers.

The smallest 3 × 3 magic square whose entries are consecutive fibodiv numbers is

The first fibodiv numbers are 14, 19, 28, 47, 61, 75, 122, 149, 183, 199, 244, 298, 305, 323, 366, 427, 488, 497, 549 more terms