cp's OEIS Frontend

A375008 Products m of k = 3 consecutive primes p_1..p_k, where only p_1 < m^(1/k).

%I A375008 #11 Sep 16 2024 12:52:39
%S A375008 105,1001,4199,20677,47027,65231,146969,190747,290177,347261,478661,
%T A375008 871933,1009091,1201289,1879981,2494633,3127361,3864241,4273697,
%U A375008 5171489,5605027,6672203,7566179,9363547,10681031,11592209,13420567,15546187,16965341,18181979,19172437
%N A375008 Products m of k = 3 consecutive primes p_1..p_k, where only p_1 < m^(1/k).
%C A375008 In other words, products m of k = 3 consecutive primes p_1..p_k, where floor(log_p_1 m) >= k but floor(log_p_j m) = k-1, j > 1.
%C A375008 For m = 105, floor(log_3 105) > k but floor(log_p_j 105) = k-1 for j > 1.
%C A375008 For m > 105, floor(log_p_1 m) = k but floor(log_p_j m) = k-1 for j > 1.
%C A375008 Superset of A372419.
%C A375008 Does not intersect A372319.
%H A375008 Michael De Vlieger, <a href="/A375008/b375008.txt">Table of n, a(n) for n = 1..10000</a>
%e A375008 105 is in the sequence since m = 3*5*7 = 105 is such that 3 is less than the cube root of 105, but both 5 and 7 exceed it.
%e A375008 385 is not in the sequence because m = 5*7*11 = 385 is such that both 5 and 7 are less than the cube root.
%e A375008 1001 is in the sequence since m = 7*11*13 = 1001 is such that 7 < 1001^(1/3), but both 11 and 13 are larger than 1001^(1/3), etc.
%t A375008 k = 3; 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]]
%Y A375008 Cf. A372209, A372319, A372419.
%K A375008 nonn,easy
%O A375008 1,1
%A A375008 _Michael De Vlieger_, Sep 11 2024