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%I #5 Sep 16 2024 12:52:57
%S 113,139,181,211,293,337,421,631,811,839,863,887,953,1021,1051,1069,
%T 1129,1259,1307,1327,1409,1471,1583,1637,1669,1759,1951,2069,2113,
%U 2179,2221,2251,2311,2423,2647,2777,2819,2939,2971,3137,3229,3271,3517,3659,3739,3779
%N Primes p_1 where products m of k = 4 consecutive primes p_1..p_k are such that only p_1 < m^(1/k).
%C Let gap g(j) = p_j - p_(j+1), j < k. Primes p_1 such that g(1) is at least as large as g(2) + g(3).
%C Proper subset of A372209.
%C Does not intersect A007530.
%H Michael De Vlieger, <a href="/A375974/b375974.txt">Table of n, a(n) for n = 1..10000</a>
%t k = 4; s = {1}~Join~Prime[Range[k - 1]]; Reap[Do[s = Append[Rest[s], Prime[i + k - 1]]; r = Surd[Times @@ s, k]; If[Count[s, _?(# < r &)] == 1, Sow[Prime[i]] ], {i, 4000}] ][[-1, 1]]
%Y Cf. A007530, A372209.
%K nonn
%O 1,1
%A _Michael De Vlieger_, Sep 12 2024