A390769 - OEIS

A390769

Least even positive integer k that does not appear in the first n prime gaps.

2, 4, 4, 6, 6, 6, 6, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16, 16

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OFFSET

1,1

COMMENTS

Erdős asks if a(n) or even a(n)/log(n) tends to infinity (see Erdős Problems link).

LINKS

Table of n, a(n) for n=1..72.

Thomas Bloom, Problem 853, Erdős Problems.

EXAMPLE

For n = 3 the first three prime gaps are {1, 2, 2} so 4 is the least even positive integer that does not appear in this set.

MATHEMATICA

a[n_]:=(k=2; g=Differences@Prime@Range[n+1]; While[MemberQ[g, k], k+=2]; k); Array[a, 70]