# How do I write this formally?

For every number N in a sequence of numbers it is true that each odd N is followed by 0 or more other numbers (not including 0) then the number N+1.

How do I write this formally?

This is my attempt but it is probably wrong.

∀ a at position b:
a is odd ∧
∃ c at position d:
d > b ∧
c = a + 1 ∧
∀ e at position f:
d > f > b ∧
e != 0

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If I understand you correctly, you have a sequence $\langle n_k:k\in\mathbb{N}\rangle$ of integers. You want to say that if $n_k$ is odd, then there is some $m>k$ such that (a) $n_m=n_k+1$, and (b) $n_i\ne 0$ whenever $k<i<m$. How you write it formally depends on what formalism you’re using, but here’s one possibility:
$$\forall k\in\mathbb{N}\left(n_k\text{ is odd}\to\exists m>k\Big(n_m=n_k+1\land\forall i\in\mathbb{N}\big(k<i<m\to a_i\ne 0\big)\Big)\right)$$
Added: You can specify beforehand that all variables and indices range only over natural numbers, so that this doesn’t have to be embedded in the description of the desired property. If the sequence is finite, and the length is known ahead of time, that too can be specified, say as $N$. Then you can write:
$$\forall k<N\left(n_k\text{ is odd}\to\exists m\Big(k<m\le N\land n_m=n_k+1\land\forall i\big(k<i<m\to a_i\ne 0\big)\Big)\right)$$