[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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