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In Python 2, making a user-defined class support formatting using the integer-specific type codes required that __int__ be defined and nothing else (that is, '%x' % Foo() only required Foo to provide a __int__ method). In Python 3, this was changed to perform the conversion via __index__ for the %o, %x and %X format types (to match how oct and hex behave), not __int__, but the pre-check for validity in unicodeobject.c's mainformatlong function is still based on PyNumber_Check, not PyIndex_Check, and PyNumber_Check is concerned solely with __int__ and __float__, not __index__.
This means that a class with __index__ but not __int__ can't be used with the %o/%x/%X format codes (even though hex(mytype) and oct(mytype) work just fine).
It seems to me that either:
1. PyNumber_Check should be a superset of PyIndex_Check (broader change, probably out of scope)
or
2. mainformatlong should restrict the scope of the PyNumber_Check test to only being used for the non-'o'/'x'/'X' tests (where it's needed to avoid coercing strings and the like to integer).
Change #2 should be safe, with no major side-effects; since PyLong and subclasses always passed the existing PyNumber_Check test anyway, and PyNumber_Index already performs PyIndex_Check, the only path that needs PyNumber_Check is the one that ends in calling PyNumber_Long.

Note: Obviously, defining __index__ without defining __int__ is a little strange (it's *equivalent* to int, but can't be *coerced* to int?), so yet another fix would be addressing #20092 so it wouldn't be possible for a type to define __index__ without (implicitly) defining __int__.

To be clear, this is a problem with old-style (printf-style) formatting, and applies to both bytes formatting and str formatting. So a class like:
 class Foo:
 def __index__(self):
 return 1
will fail with a TypeError should you do any of:
 '%o' % Foo()
 '%x' % Foo()
 '%X' % Foo()
 b'%o' % Foo()
 b'%x' % Foo()
 b'%X' % Foo()
even though hex(Foo()) and oct(Foo()) work without issue.

Agreed that this seems wrong.

Resolved in issue36048.