This section defines the set A. the following sections use this definition to study the set itself and study the consequences on other similar sets. But first let us define the set:

\[A=\{a_n=a_{n-1}+n;a_0=1;n\in \mathbb{N}\}\]

This set is infinite and starts at 1. The following table gives an overview of the first elements:

\(a_n\) | \(n\) |

1 | 0 |

2 | 1 |

4 | 2 |

7 | 3 |

11 | 4 |

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