A376440 Smallest primes p_1 where products m of n consecutive primes p_1..p_n are such that only p_n > m^(1/n).

2, 2, 107, 1657, 25453, 404819, 1388449, 137414987, 402301129, 87241770523

Offset: 2

Author

Michael De Vlieger, Sep 22 2024

Keywords

• nonn
• hard
• more

Examples

			a(2) = 2 since m = 2*3 = 6 and 2 < sqrt(6).
a(3) = 2 since m = 2*3*5 = 30 and 3 < 30^(1/3).
a(4) = 107 since m = 107 * 109 * 113 * 127 = 167375713 and 113 < 167375713^(1/4), etc.
		

Crossrefs

Cf. A374873.

Programs

Mathematica

k = 1; Table[r = Range[0, n - 1]; While[(Set[{p, q, m}, {#[[1]], #[[-2]], Times @@ #}]; q > Surd[m, n]) &[Prime[k + r]], k++]; p, {n, 2, 6}]

PARI

a(n) = {my(ps = vector(n, k, prime(k))); forprime(p = prime(n+1), , if(ps[#ps-1]^n < vecprod(ps), return(ps[1])); ps = concat(vecextract(ps, "^1"), p));} \\ Amiram Eldar, Sep 23 2024

Extensions

a(10)-a(11) from Amiram Eldar, Sep 23 2024