Kynea numbers

oeis/__init__.py

@@ -23,6 +23,7 @@
 from .factorial import factorial
 from .fibonacci import fibonacci
 from .jacobsthal import jacobsthal
+from .kynea import kynea
 from .lazy_caterer import lazy_caterer
 from .leonardo import leonardo
 from .loeschian import loeschian
@@ -95,6 +96,7 @@
     "hexagonal",
     "hexagonal_pyramidal",
     "jacobsthal",
+    "kynea",
     "lazy_caterer",
     "leonardo",
     "loeschian",

oeis/kynea.py

@@ -0,0 +1,12 @@
+# coding=utf-8
+from itertools import count
+from typing import Iterable
+
+from oeis.registry import registry
+
+
+@registry.register("A093069")
+def kynea() -> Iterable[int]:
+    """Kynea numbers."""
+    for n in count(start=1):
+        yield pow(pow(2, n) + 1, 2) - 2

tests/test_oeis.py

@@ -31,6 +31,7 @@
     hexagonal,
     hexagonal_pyramidal,
     jacobsthal,
+    kynea,
     lazy_caterer,
     leonardo,
     loeschian,
@@ -232,6 +233,12 @@ def test_jacobsthal() -> None:
     assert actual == expected
 
 
+def test_kynea() -> None:
+    expected: List[int] = [7, 23, 79, 287, 1087, 4223, 16639, 66047, 263167, 1050623]
+    actual: List[int] = list(islice(kynea(), 10))
+    assert actual == expected
+
+
 def test_lazy_caterer() -> None:
     expected: List[int] = [1, 2, 4, 7, 11, 16, 22, 29, 37, 46]
     actual: List[int] = list(islice(lazy_caterer(), 10))