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Fungrim entry: b7e899

Bn+a≡Bn(modm)   where a=A054767 ⁣(m)B_{n + a} \equiv B_{n} \pmod {m}\; \text{ where } a = \text{A054767}\!\left(m\right)
Assumptions:n∈Z≥0  and⁡  m∈Z≥1n \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
BellNumberBnB_{n} Bell number
SloaneAA00000X ⁣(n)\text{A00000X}\!\left(n\right) Sequence X in Sloane's OEIS
ZZGreaterEqualZ≥n\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