A390769 - OEIS

%I #10 Nov 25 2025 21:18:34

%S 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,

%T 10,10,10,12,12,12,12,12,12,12,12,12,12,12,12,16,16,16,16,16,16,16,16,

%U 16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16,16

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

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

%H Thomas Bloom, <a href="https://www.erdosproblems.com/853">Problem 853</a>, Erdős Problems.

%e 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.

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

%Y Cf. A000040, A000101, A001223, A002386, A005250.

%K nonn

%O 1,1

%A _Giorgos Kalogeropoulos_, Nov 18 2025