weak prime

If for the given $n$ th prime $p_{n}$ the inequality

p_{n}<{1\over 3}\sum_{i=n-1}^{n+1}p_{i}

is true, then $p_{n}$ is said to be a weak prime. That is, the arithmetic mean of the given prime, the prime immediately below and the one immediately above, is more than the middle prime. The first few are 3, 7, 13, 19, 23, 31, 43, 47, 61, 73, 83, 89, listed in A051635 of Sloane’s OEIS.

Title	weak prime
Canonical name	WeakPrime
Date of creation	2013-03-22 16:36:56
Last modified on	2013-03-22 16:36:56
Owner	PrimeFan (13766)
Last modified by	PrimeFan (13766)
Numerical id	4
Author	PrimeFan (13766)
Entry type	Definition
Classification	msc 11A41
Related topic	BalancedPrime
Related topic	StrongPrime