# Fungrim entry: b7e899

$B_{n + a} \equiv B_{n} \pmod {m}\; \text{ where } a = \text{A054767}\!\left(m\right)$
Assumptions:$n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; m \in \mathbb{Z}_{\ge 1}$
References:
• Sequence A054767 in Sloane's On-Line Encyclopedia of Integer Sequences (OEIS)
TeX:
B_{n + a} \equiv B_{n} \pmod {m}\; \text{ where } a = \text{A054767}\!\left(m\right)

n \in \mathbb{Z}_{\ge 0} \;\mathbin{\operatorname{and}}\; m \in \mathbb{Z}_{\ge 1}
Definitions:
Fungrim symbol Notation Short description
BellNumber$B_{n}$ Bell number
SloaneA$\text{A00000X}\!\left(n\right)$ Sequence X in Sloane's OEIS
ZZGreaterEqual$\mathbb{Z}_{\ge n}$ Integers greater than or equal to n
Source code for this entry:
Entry(ID("b7e899"),
Formula(Where(CongruentMod(BellNumber(Add(n, a)), BellNumber(n), m), Equal(a, SloaneA("A054767", m)))),
Variables(n, m),
Assumptions(And(Element(n, ZZGreaterEqual(0)), Element(m, ZZGreaterEqual(1)))))

## Topics using this entry

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