I'm new to Python and want to write a function that accepts a positive integer range and outputs every number that is either prime or equal to a prime multiplied by a power of two. Pure powers of two should count as well, since they can be written as 1 × 2^n. For example, the range 8 through 16 should produce 8 (2^3), 10 (5 × 2^1), 11, 12 (3 × 2^2), 13, 14 (7 × 2^1), and 16 (2^4). What would be a simple way to implement this?
4 Answers
Before writing the filtering logic, decide what “range” means. The example includes both 8 and 16, so the code should include the upper endpoint. Also, “pick” appears to mean print or return all matching numbers rather than randomly choose one.
A useful approach is to repeatedly divide each number by 2 while it is even. The remaining odd part will be either 1 or a prime if the original number matches your rule. You can then test that odd part with a basic prime-checking function.
You can also think of each number as `odd_part × 2^k`. Removing factors of two leaves the odd part. For example, 12 becomes 3 after dividing by 2 twice, so it qualifies because 3 is prime. This is easier to understand at first than using bit operations; optimizations such as shifting bits can come later.
Here is a straightforward implementation. This version treats both range endpoints as included and considers powers of two valid by allowing the remaining value to be 1:
```python
def is_prime(n):
if n < 2:
return False
for divisor in range(2, int(n ** 0.5) + 1):
if n % divisor == 0:
return False
return True
def is_special(n):
while n % 2 == 0:
n //= 2
return n == 1 or is_prime(n)
def special_numbers(start, end):
return [n for n in range(start, end + 1) if is_special(n)]
print(special_numbers(8, 16))
```
The output is `[8, 10, 11, 12, 13, 14, 16]`. In Python, `range(start, end + 1)` is used here because the normal end value is excluded.
I’m completely new to coding, so I’ll probably start with a simple Python editor and first learn how to loop through and print a range.