[seqfan] Re: The function of status "prime-noprime" of n: 2^A082495-1^062173(n).

[Joerg Arndt]

* юрий герасимов <2stepan at rambler.ru> [Jan 08. 2011 15:10]:
> Hello,
> 
> Numbers n=primes such that 2^((2^n-1) mod n)-1^(2^(n-1) mod n)=1 and
> numbers n=nonprimes such that 2^((2^n-1) mod n)-1^(2^(n-1) mod n)<>1
> ?
> 
> Tranke you,
> JSG,
> 

So before you even know the truth of the statement
you started the edit  http://oeis.org/draft/A141468

Charming.


Here is the conjecture as I understand it:
Let f(n) = 2^((2^n-1) mod n) - 1^(2^(n-1) mod n)
then  f(n) == 1 if and only if n is prime.


First counterexample: n=341, infinitely many more in A001567

? for(n=1,10000,if(2^((2^n-1) % n)-1^(2^(n-1) % n)==1 && !isprime(n),print(n)))
341 561 645 1105 1387 1729 1905 2047 2465 2701 2821 3277 4033 4369
4371 4681 5461 6601 7957 8321 8481 8911