A309329 Median of primes with n decimal digits.

4, 47, 509, 5273, 53047, 532887, 5356259, 53765483, 539119753, 5402600081, 54118210435, 541947386821, 5425907665571, 54313871643797, 543611236251491, 5440228524355329, 54438462600610510, 544705097744731559, 5449909581264135103

Offset: 1

Author

Hugo Pfoertner, Jul 25 2019

Keywords

• nonn
• base
• more

Comments

The number of n-digit primes < a(n) equals the number of n-digit primes > a(n). The median of an even number of values is understood to be defined as the arithmetic mean of the two central elements.

Examples

			a(1) = 4 because {2, 3, 5, 7} are the 4 one-digit primes. The 2 central elements of the sorted list are 3 and 5. 4 = (3 + 5)/2.
a(2) = 47 because it is the central element of the sorted list of the A006879(2) = 21 two-digit primes. There are 10 such primes < 47 and 10 such primes > 47.
		

Crossrefs

Cf. A006879, A006880, A309359

Formula

a(n) = (prime(A006880(n-1) + ceiling(A006879(n)/2)) + prime(A006880(n-1) + floor(A006879(n)/2) + 1)) / 2.