Common Values of Padovan and Perrin Sequences
The integer sequence defined by P n + 3 = P n + 1 + P n with initial conditions P 0 = P 1 = P 2 = 1 is known as the Padovan sequence ( P n ) n ∈ Z . The Perrin sequence ( R m ) m ∈ Z satisfies the same recurrence equation as the Padovan sequence but with starting values R 0 = 3 , R 1 = 0 , and R 2 =...
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| Published in: | Mediterranean journal of mathematics 2023-10, Vol.20 (5), Article 268 |
|---|---|
| Main Author: | |
| Format: | Article |
| Language: | eng |
| Subjects: | |
| Online Access: | Get full text |
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| Summary: | The integer sequence defined by
P
n
+
3
=
P
n
+
1
+
P
n
with initial conditions
P
0
=
P
1
=
P
2
=
1
is known as the Padovan sequence
(
P
n
)
n
∈
Z
. The Perrin sequence
(
R
m
)
m
∈
Z
satisfies the same recurrence equation as the Padovan sequence but with starting values
R
0
=
3
,
R
1
=
0
, and
R
2
=
2
. In this note, we solve the Diophantine equation
P
n
=
±
R
m
with
(
n
,
m
)
∈
Z
2
. |
|---|---|
| ISSN: | 1660-5446 1660-5454 |