Elliptic Divisibility Sequence - Examples

Examples

A simple example of an EDS is the sequence of natural numbers 1, 2, 3,… . Another interesting example is the sequence 1, 3, 8, 21, 55, 144, 377, 987,… consisting of every other term in the Fibonacci sequence, starting with the second term. However, both of these sequences satisfy a linear recurrence and both are singular EDS. An example of a nonsingular EDS is

\begin{align} &1,\, 1,\, -1,\, 1,\, 2,\, -1,\, -3,\, -5,\, 7,\, -4,\, -23,\, 29,\, 59,\, 129,\\ &-314,\, -65,\, 1529,\, -3689,\, -8209,\, -16264,\dots.\\ \end{align}

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