A372209 Primes p_1 where products m of k = 3 consecutive primes p_1..p_k are such that only p_1 < m^(1/k).

3, 7, 13, 23, 31, 37, 47, 53, 61, 67, 73, 89, 97, 103, 113, 131, 139, 151, 157, 167, 173, 181, 193, 199, 211, 223, 233, 241, 251, 257, 263, 271, 277, 293, 307, 317, 337, 359, 367, 373, 389, 409, 421, 433, 449, 457, 467, 479, 491, 509, 523, 547, 557, 563, 577, 587

Offset: 1

Author

Michael De Vlieger, Sep 11 2024

Keywords

• nonn
• easy

Comments

Primes p such that the second differences of p and the next 2 primes is never positive.

Superset of A022005.

Does not intersect A022004.

Examples

			3 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.
5 is not in the sequence because m = 5*7*11 = 385 is such that both 5 and 7 are less than the cube root.
7 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.
		

Links

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

Crossrefs

Cf. A022004, A022005, A375008.

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[Prime[i]] ], {i, 600}] ][[-1, 1]]