# Completely Random Sequence

Discrete Mathematics Level pending

Are there any infinite sequences of numbers that are not defined by a finite number of symbols from the English alphabet?

For example: $$1, 104, 4372, 96256, 1240002, ...$$ is a sequence whose definition is the expansion of $$\frac{16(1+k^2)^4}{(k\cdot k'^2)^2}$$ in powers of $$q$$ where $$k$$ is the Jacobian elliptic modulus, $$k'$$ the complementary modulus and $$q$$ is the nome.

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