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A376261
Products m of k = 5 consecutive primes p_1..p_k, where only p_1 < m^(1/k).
3
362469273063260281, 390268963330916339, 2501104163586622303, 9136139450993677127, 14786802713701223291, 16175430816211360949, 42275879149134880507, 58976503686022007233, 75786488186892877007, 124796858811854774081, 226284602311169194703, 252607170708747107509
OFFSET
1,1
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
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]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael De Vlieger, Sep 17 2024
STATUS
approved