From a9364c97a3d9d5637eccae168bd60914f0a77d26 Mon Sep 17 00:00:00 2001
From: Kshitij Saraogi <kshitij.saraogi@gmail.com>
Date: Wed, 22 Nov 2023 09:00:44 +0100
Subject: [PATCH] feat: Implement A065722 Paterson Primes (#391)

---
 oeis.py               | 23 +++++++++++++++
 tests/test_A065722.py | 65 +++++++++++++++++++++++++++++++++++++++++++
 2 files changed, 88 insertions(+)
 create mode 100644 tests/test_A065722.py

diff --git a/oeis.py b/oeis.py
index d757e35..e74422a 100644
--- a/oeis.py
+++ b/oeis.py
@@ -97,6 +97,11 @@ def __getitem__(self, key: Union[int, slice]) -> Union[int, Sequence[int]]:
         """Return a slice or a value from an integer sequence."""
         raise NotImplementedError
 
+    def __iter__(self) -> Iterator[int]:
+        """Iterate over the integer sequence."""
+        for i in count(self.offset):
+            yield self[i]
+
 
 class IntegerSequenceFromGenerator(IntegerSequence):
     """IntegerSequence based on a generator.
@@ -752,6 +757,24 @@ def A002182() -> Iterable[int]:
             yield n
 
 
+@oeis.from_generator(offset=0)
+def A065722() -> Iterable[int]:
+    """Primes that when written in base 4, then reinterpreted in base 10, again give primes."""
+    for p in A000040:  # pylint: disable=not-an-iterable
+        # Refer: https://github.com/pylint-dev/pylint/issues/9251
+        if _is_patterson_prime(p):
+            yield p
+
+
+def _is_patterson_prime(n):
+    import numpy as np
+    from sympy.ntheory import isprime
+
+    base_four_repr = np.base_repr(n, base=4)
+    base_ten_repr = int(base_four_repr)
+    return isprime(base_ten_repr)
+
+
 def main() -> None:  # pylint: disable=too-many-branches
     """Command line entry point."""
     args = parse_args()
diff --git a/tests/test_A065722.py b/tests/test_A065722.py
new file mode 100644
index 0000000..ab6cb80
--- /dev/null
+++ b/tests/test_A065722.py
@@ -0,0 +1,65 @@
+from oeis import A065722
+
+
+def test_A065722():
+    from_oeis_org = [
+        2,
+        3,
+        5,
+        7,
+        11,
+        13,
+        17,
+        19,
+        23,
+        29,
+        37,
+        43,
+        47,
+        53,
+        61,
+        71,
+        73,
+        79,
+        83,
+        97,
+        103,
+        107,
+        109,
+        113,
+        131,
+        149,
+        151,
+        157,
+        163,
+        167,
+        181,
+        191,
+        193,
+        197,
+        227,
+        233,
+        241,
+        251,
+        277,
+        293,
+        307,
+        311,
+        313,
+        317,
+        349,
+        359,
+        373,
+        389,
+        401,
+        419,
+        421,
+        433,
+        443,
+        449,
+        463,
+        467,
+        503,
+    ]
+
+    assert A065722[: len(from_oeis_org)] == from_oeis_org