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.

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