A318554 a(n) is the smallest prime number having order of primeness = prime(n).

3, 5, 31, 709, 9737333, 3657500101, 2586559730396077, 4123221751654370051, 28785866289100396890228041

Offset: 1

Author

David James Sycamore, Aug 27 2018

Keywords

• nonn
• more

Comments

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).

Examples

			The sequence of primes with order of primeness F(p) = prime(1) = 2 begins 3,17,41,67,...
so a(1)=3. Likewise, F(p) = prime(2) = 3 begins 5,59,179,... so a(2)=5.
		

Links

• N. Fernandez, An order of primeness, F(p)
• N. Fernandez, An order of primeness [cached copy, included with permission of the author]

Crossrefs

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

Formula

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