Wild number  Originally, wild numbers are the numbers supposed to belong to a fictional sequence of numbers imagined to exist in the mathematical world of the mathematical fiction "The Wild Numbers" authored by Philibert Schogt, a Dutch philosopher and mathematician. Even though Schogt has given a definition of the wild number sequence in his novel, it is couched in a deliberately imprecise language that the definition turns out to be no definition at all. However, the author claims that the first few members of the sequence are 11, 67, 2, 4769, 67. Later, inspired by this wild and erratic behaviour of the fictional wild numbers, American mathematician J. C. Lagarias used the terminology to describe a precisely defined sequence of integers which shows somewhat similar wild and erratic behaviour. Lagaria's wild numbers are connected with the Collatz conjecture and the concept of the 3"x" + 1 semigroup. The original fictional sequence of wild numbers has found a place in the On-Line Encyclopedia of Integer Sequences. In the novel "The Wild Numbers", The Wild Number Problem is formulated as follows:   But it has not been specified what those "deceptively simple operations" are. Consequently, there is no way of knowing how those numbers 11, 67, etc. were obtained and no way of finding what the next wild number would be. The novel "The Wild Numbers" has constructed a fictitious history for The Wild Number Problem. The important milestones in this history can be summarised as follows. In mathematics, the multiplicative semigroup, denoted by "W"0, generated by the set formula_1 is called the Wooley semigroup in honour of the American mathematician Trevor D. Wooley. The multiplicative semigroup, denoted by "W", generated by the set formula_2 is called the wild semigroup. The set of integers in "W"0 is itself a multiplicative semigroup. It is called the Wooley integer semigroup and members of this semigroup are called Wooley integers. Similarly, the set of integers in "W" is itself a multiplicative semigroup. It is called the wild integer semigroup and members of this semigroup are called wild numbers. The On-Line Encyclopedia of Integer Sequences (OEIS) has an entry with the identifying number relating to the wild numbers. According to OEIS, "apparently these are completely fictional and there is no mathematical explanation". However, the OEIS has some entries relating to pseudo-wild numbers carrying well-defined mathematical explanations.