# [seqfan] Re: Emirps (sorted by period) with with unique period length

Ray Chandler rayjchandler at sbcglobal.net
Tue Oct 12 16:56:16 CEST 2010

```
>
> 37, 333667, 909091
>
> no more through A007615(15).
>
> A007615 INTERSECTION A006567.
>
> Primes p whose reversal is a different prime, and which are
> the only primes p = A007615 (n) such that decimal expansion
> of 1/p has unique
> (nontrivial) period A007498 (A007615(n)).
>
> Examples:
> a(1) = 37 because R(37) = 73 is prime, and 37 is the unique
> prime p such that 1/p has period 1/37 = 3.
> a(2) = 333667 because R(333667) = 766333 is prime, and 333667
> is the unique prime p such that 1/p has period 1/333667 = 9.
> a(3) = 909091 because R(909091) = 190909 is prime, and 909091
> is the unique prime p such that 1/p has period 1/909091 = 14.
>
>
> Base. More.
>
> Cf. 000040, A004086, A006567, A007498, A007615.
>

a(4)=99999999999999000000000000009999999999999900000000000000999999999999990
0000000000001
(84 digits).
R(a(4))=10000000000000999999999999990000000000000099999999999999000000000000
0099999999999999
is prime.
a(4) is unique prime such that 1/p has period 84.

No others through known unique periods using b-file from A007498.
Ray

```