1
$\begingroup$

A positive integer is said to be strange if all powers are odd in their prime factorisation. For instance, $22,23,24$ form a block of consecutive strange numbers because $22=2^1\times11^1,23=23^1,24=2^3\times3^1$. What is the greatest length of a block of consecutive strange numbers?

I tried all the numbers till 50 and obtained two series with $7$ terms which is the answer. The consecutive numbers are:- $$S_1=29,30,31,32,33,34,35\\S_2=37,38,39,40,41,42,43$$How can we make sure that we cannot find any series with more than $7$ terms?

$\endgroup$
3
  • 4
    $\begingroup$ If x is 4 mod 8, then x is not strange. $\endgroup$
    – Eric
    May 29 at 3:03
  • $\begingroup$ Do you mean that all the exponents in the prime factorizations are odd ? $\endgroup$
    – Peter
    May 30 at 9:33
  • $\begingroup$ @Eric Why not formulate this as an answer ? I would galdly upvote it. $\endgroup$
    – Peter
    May 30 at 9:35
1
$\begingroup$

If x is 4 mod 8, then x is not strange. Therefore, you can’t have a sequence of 8 consecutive strange numbers.

$\endgroup$

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.