A375974 Primes p_1 where products m of k = 4 consecutive primes p_1..p_k are such that only p_1 < m^(1/k).

113, 139, 181, 211, 293, 337, 421, 631, 811, 839, 863, 887, 953, 1021, 1051, 1069, 1129, 1259, 1307, 1327, 1409, 1471, 1583, 1637, 1669, 1759, 1951, 2069, 2113, 2179, 2221, 2251, 2311, 2423, 2647, 2777, 2819, 2939, 2971, 3137, 3229, 3271, 3517, 3659, 3739, 3779

Offset: 1

Author

Michael De Vlieger, Sep 12 2024

Keywords

• nonn

Comments

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).

Proper subset of A372209.

Does not intersect A007530.

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007530, A372209.

Programs

Mathematica

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]]