A376261 Products m of k = 5 consecutive primes p_1..p_k, where only p_1 < m^(1/k).

362469273063260281, 390268963330916339, 2501104163586622303, 9136139450993677127, 14786802713701223291, 16175430816211360949, 42275879149134880507, 58976503686022007233, 75786488186892877007, 124796858811854774081, 226284602311169194703, 252607170708747107509

Offset: 1

Author

Michael De Vlieger, Sep 17 2024

Keywords

• nonn

Comments

In other words, products m of k = 5 consecutive primes p_1..p_k, where floor(log_p_1 m) >= k but floor(log_p_j m) = k-1, j > 1.

a(n) = m is such that floor(log_p_1 m) = k but floor(log_p_j m) = k-1 for j > 1.

Contains neither A375263 nor A375264, since for m in either sequence, both p_1 and p_2 are smaller than m^(1/k).

Links

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

Crossrefs

Cf. A375263, A375264, A376136.

Programs

Mathematica

k = 5; 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[Times @@ s] ], {i, 120}] ][[-1, 1]]