[seqfan] Climb to a prime, yet another way.

Antti Karttunen antti.karttunen at gmail.com
Wed Jun 21 08:41:19 CEST 2017

Cheers all,

I offer €42 for the first proof or disproof of the conjecture I make
in https://oeis.org/A087207 that starting with any natural number n >=
1, iterations of A087207 ("A binary representation of the primes that
divide a number, shown in decimal") eventually lead to zero. That is,
if we start from any n that itself is neither a prime nor a power of
two, we will eventually hit a prime number.

For a simple disproof, show me a number n for which a positive number
of applications of A087207 will lead back to the same n.

For a purely existential proof that at least one such cycle exists or
that some trajectory can never reach zero, please publish a paper in a
generally respected peer-reviewed mathematical journal.
Likewise if you have a proof that all iterations of A087207 reach zero.

(Funny thought: Can we make conjectures more popular by offering money
for their solutions?)

Best regards,

Antti Karttunen

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