A318554 - OEIS

%I #13 Nov 02 2018 06:42:29

%S 3,5,31,709,9737333,3657500101,2586559730396077,4123221751654370051,

%T 28785866289100396890228041

%N a(n) is the smallest prime number having order of primeness = prime(n).

%C Let F(k) denote A049076(k). The list of primes p such that F(p) = n begins with q, the smallest prime to have prime index in each of n-1 successive primeth iterations, finally taking nonprime index 1 at the n-th iteration. All other members p such that F(p) = n are primes > q which also take a nonprime index at the n-th iteration. The reverse sequence of associated indices for q = prime(n) gives successive terms of the primeth recurrence 1,2,3,5,... until reaching A007097(prime(n)) = a(n).

%H N. Fernandez, <a href="http://www.borve.org/primeness/FOP.html">An order of primeness, F(p)</a>

%H N. Fernandez, <a href="/A006450/a006450.html">An order of primeness</a> [cached copy, included with permission of the author]

%F a(n) = A007097(prime(n)); n >= 1.

%e The sequence of primes with order of primeness F(p) = prime(1) = 2 begins 3,17,41,67,...

%e so a(1)=3. Likewise, F(p) = prime(2) = 3 begins 5,59,179,... so a(2)=5.

%Y Cf. A000040, A006450, A007097, A049076, A049078, A049079, A049081.

%K nonn,more

%O 1,1

%A _David James Sycamore_, Aug 27 2018