cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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

Original entry on oeis.org

105, 1001, 4199, 20677, 47027, 65231, 146969, 190747, 290177, 347261, 478661, 871933, 1009091, 1201289, 1879981, 2494633, 3127361, 3864241, 4273697, 5171489, 5605027, 6672203, 7566179, 9363547, 10681031, 11592209, 13420567, 15546187, 16965341, 18181979, 19172437
Offset: 1

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Author

Michael De Vlieger, Sep 11 2024

Keywords

Comments

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.
For m = 105, floor(log_3 105) > k but floor(log_p_j 105) = k-1 for j > 1.
For m > 105, floor(log_p_1 m) = k but floor(log_p_j m) = k-1 for j > 1.
Superset of A372419.
Does not intersect A372319.

Examples

			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.
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.
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.
		

Crossrefs

Programs

  • Mathematica
    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]]
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