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Fungrim entry: 050ee1

Bn≡{0,n≡2(mod3)1,otherwise(mod2)B_{n} \equiv \begin{cases} 0, & n \equiv 2 \pmod {3}\\1, & \text{otherwise}\\ \end{cases} \pmod {2}
Assumptions:n∈Z≥0n \in \mathbb{Z}_{\ge 0}
TeX:
B_{n} \equiv \begin{cases} 0, & n \equiv 2 \pmod {3}\\1, & \text{otherwise}\\ \end{cases} \pmod {2}

n \in \mathbb{Z}_{\ge 0}
Definitions:
Fungrim symbol Notation Short description
BellNumberBnB_{n} Bell number
ZZGreaterEqualZ≥n\mathbb{Z}_{\ge n} Integers greater than or equal to n
Source code for this entry:
Entry(ID("050ee1"),
    Formula(CongruentMod(BellNumber(n), Cases(Tuple(0, CongruentMod(n, 2, 3)), Tuple(1, Otherwise)), 2)),
    Variables(n),
    Assumptions(Element(n, ZZGreaterEqual(0))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2021-03-15 19:12:00.328586 UTC