2n1

2n1 is most commonly encountered in mathematics as a typographical variant of the expression 2n+1, which is used to generate odd integers. When n ranges over the integers, 2n+1 yields all odd numbers: ..., -3, -1, 1, 3, 5, .... If n is restricted to nonnegative integers, it yields the positive odd numbers: 1, 3, 5, 7, ...

In modular arithmetic, an integer m is odd if and only if there exists an integer n with m = 2n+1. Conversely, every odd integer can be written in this form with n = (m−1)/2. The representation 2n+1 thus characterizes oddness algebraically and provides a convenient way to index odd terms in sequences or algorithms.

Applications of this form appear throughout number theory and related fields. It underpins parity arguments in proofs, and in primality considerations, any odd prime p can be expressed as p = 2n+1 for some n = (p−1)/2. The expression also serves in generating sequences of odd numbers, in algebraic manipulations, and in computer algorithms that iterate over odd positions or values.

Ambiguity may arise with the string 2n1 lacking a plus sign. In most mathematical contexts, the intended meaning is 2n+1, and 2n1 should be treated as potentially a typographical error or as an unrelated identifier rather than a standard mathematical form.