Nicholas (nwhyte) wrote,
Nicholas
nwhyte

Consecutive integers with the same number of factors

The numbers 2 and 3 are both prime, so both have two factors, themselves and 1.
23
11

While there are no other examples of consecutive primes, it's not difficult to find more pairs of consecutive integers with the same number of factors:
1415
75
23
11
    
2122
711
32
11

Eventually you get to sets of three consecutive integers with the same number of factors:
333435
11177
325
111
    
858687
174329
523
111

It isn't possible to have a sequence of more than three integers with only four factors, but so far I have found this set of four consecutive integers with six factors:
242243244245
1218112249
22276135
11947
2325
1111

I'm sure that somewhere out there I can find out whether or not a) there are longer sequences of consecutive integers which the same number of factors and b) whether there is a natural limit to the process. That's as far as I can take it in the sleepless hours of the night though.
Subscribe
  • Post a new comment

    Error

    default userpic

    Your reply will be screened

    Your IP address will be recorded 

    When you submit the form an invisible reCAPTCHA check will be performed.
    You must follow the Privacy Policy and Google Terms of use.
  • 3 comments