Miseryint

Miseryint, also known as "misery integer," is a concept in number theory and recreational mathematics that refers to a positive integer which, when multiplied by a certain number of consecutive integers, results in a number that is the reverse of the original integer. For example, 142857 is a misery integer because it multiplied by 1, 2, 3, 4, 5, and 6 yields 142857, 285714, 428571, 571428, 714285, and 857142, respectively, which are all permutations of the digits of 142857.

The term "misery integer" was coined by mathematician John Conway. Misery integers are rare and have been found only for specific values. The smallest known misery integer is 142857, which is also known as the "magic number" in some contexts. Other known misery integers include 217852 and 588235.

Misery integers are of interest to mathematicians and number enthusiasts due to their unique properties and the challenge of finding them. The search for new misery integers remains an active area of research in number theory.