What composite number can be represented as $binomnk$ for $kneq1$ or $n-1$

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This is a problem I came up with when I was working with binomial coefficients. Let's call the title statement $(*)$. Obviously for any primes do not satisfy $(*)$, therefore we only need to focus on composite numbers.



How can I proceed?



Any help appreciated.




binomial-coefficients combinatorial-number-theory




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    oeis.org/A006987
    – JMoravitz
    Jul 20 at 1:07










  • Thank you for the link! But I hope that one can analyse these numbers instead of listing them.
    – abc...
    Jul 20 at 1:11














up vote
0
down vote

favorite












This is a problem I came up with when I was working with binomial coefficients. Let's call the title statement $(*)$. Obviously for any primes do not satisfy $(*)$, therefore we only need to focus on composite numbers.



How can I proceed?



Any help appreciated.




binomial-coefficients combinatorial-number-theory




share|cite|improve this question















  • 1




    oeis.org/A006987
    – JMoravitz
    Jul 20 at 1:07










  • Thank you for the link! But I hope that one can analyse these numbers instead of listing them.
    – abc...
    Jul 20 at 1:11












up vote
0
down vote

favorite









up vote
0
down vote

favorite











This is a problem I came up with when I was working with binomial coefficients. Let's call the title statement $(*)$. Obviously for any primes do not satisfy $(*)$, therefore we only need to focus on composite numbers.



How can I proceed?



Any help appreciated.




binomial-coefficients combinatorial-number-theory




share|cite|improve this question











This is a problem I came up with when I was working with binomial coefficients. Let's call the title statement $(*)$. Obviously for any primes do not satisfy $(*)$, therefore we only need to focus on composite numbers.



How can I proceed?



Any help appreciated.





binomial-coefficients combinatorial-number-theory





share|cite|improve this question










share|cite|improve this question




share|cite|improve this question









asked Jul 20 at 1:04









abc...

1,190524




1,190524







  • 1




    oeis.org/A006987
    – JMoravitz
    Jul 20 at 1:07










  • Thank you for the link! But I hope that one can analyse these numbers instead of listing them.
    – abc...
    Jul 20 at 1:11












  • 1




    oeis.org/A006987
    – JMoravitz
    Jul 20 at 1:07










  • Thank you for the link! But I hope that one can analyse these numbers instead of listing them.
    – abc...
    Jul 20 at 1:11







1




1




oeis.org/A006987
– JMoravitz
Jul 20 at 1:07




oeis.org/A006987
– JMoravitz
Jul 20 at 1:07












Thank you for the link! But I hope that one can analyse these numbers instead of listing them.
– abc...
Jul 20 at 1:11




Thank you for the link! But I hope that one can analyse these numbers instead of listing them.
– abc...
Jul 20 at 1:11















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