[seqfan] Re: primes in A226181
Vladimir Shevelev
shevelev at bgu.ac.il
Tue May 27 20:52:47 CEST 2014
Dear Seqfans,
I have not noted immediately that a disproof of my conjecture is easily
obtained using a great Artin's conjecture. If 2 is a primitive root of prime p,
then the period of 1/p in binary expansion is p-1. So primes with primitive
root 2 (A001122) are in A226181, and, by Artin's conjecture,
lim inf (pi_1(x)/pi(x))>=C_Artin=0.3739558...
It is interesting to find an approximation of lim inf (pi_1(x)/pi(x)).
Regards,
Vladimir
________________________________________
From: SeqFan [seqfan-bounces at list.seqfan.eu] on behalf of Vladimir Shevelev [shevelev at exchange.bgu.ac.il]
Sent: 27 May 2014 14:25
To: seqfan at list.seqfan.eu
Subject: [seqfan] primes in A226181
How many actually primes in sequence A226181 ? Let pi_1(x) be number of A226181
primes not exceeding x. I believe that pi_1(x)=o(pi(x)), where
pi(x) is the counting function of all primes and x goes to infinity. Is'nt it?
Regards,
Vladimir
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