In Abraham Verghese’s 2009 novel Cutting for Stone, a character declares that 10213223 “is the only number that describes itself when you read it. ‘One zero, two ones, three twos, and two threes!'”

Refining that a bit, we can imagine a number N in which the first digit counts the number of zeroes in N, the second counts the number of ones, and so on. Such numbers are called autobiographical, and they’re remarkably few: 1210, 2020, 21200, 3211000, 42101000, 521001000, 6210001000.

But numbers needn’t look only inward — MIT mathematician Tanya Khovanova identified these “mutually praising” pairs, which inventory one another’s contents:

6300000100 and 7101001000
130 and 1101
2210 and 11200

“These numbers are too shy to advertise themselves,” she writes. “But Alice praises Bob, because Bob praises Alice. It’s a very advantageous flattery pattern!”

(Tanya Khovanova, “Autobiographical Numbers,” arXiv preprint arXiv:0803.0270 [2008]. Somewhat similar: John Conway’s “look and say” sequence.)