A056127 Minimum m where product_{k=1 to m}[p_k] > (p_{m+1})^n, where p_k is k-th prime.

1, 2, 4, 5, 7, 8, 10, 11, 13, 14, 15, 16, 18, 19, 20, 21, 23, 24, 25, 26, 28, 29, 30, 32, 33, 34, 35, 36, 38, 39, 40, 41, 43, 44, 45, 46, 48, 49, 50, 51, 52, 53, 55, 56, 57, 58, 59, 60, 62, 63, 64, 65, 67, 68, 69, 70, 72, 73, 74, 75, 76, 78, 79, 80, 81, 82, 83, 85, 86, 87, 88

Offset

0,2

Links

Eric M. Schmidt, Table of n, a(n) for n = 0..10000

Safia Aoudjit and Djamel Berkane, Explicit Estimates Involving the Primorial Integers and Applications, J. Int. Seq., Vol. 24 (2021), Article 21.7.8.

Example

a(2) = 4, since 2*3*5 < 7^2, but 2*3*5*7 > 11^2. (The product of the first 4 primes is greater than the 5th prime squared.)

Mathematica

a = {}; Do[x = 1; While[Prime[x + 1] >= (Product[Prime[x], {x, 1, x}])^(1/n), x++ ]; AppendTo[a, x], {n, 1, 100}]; a (* Artur Jasinski, May 11 2007 *)

Crossrefs

Cf. A002110, A060797, A127600, A127601, A127602, A127603, A127604.

Sequence in context: A186515 A078934 A026496 * A186352 A186157 A072633

Adjacent sequences: A056124 A056125 A056126 * A056128 A056129 A056130

Keyword

nonn

Author

Leroy Quet, Aug 30 2000

Status

approved