A111684 Least k such that the product of n consecutive integers beginning with k exceeds n^n.

2, 2, 3, 3, 4, 4, 5, 5, 6, 6, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 13, 14, 15, 15, 16, 16, 17, 17, 18, 18, 19, 19, 20, 21, 21, 22, 22, 23, 23, 24, 24, 25, 25, 26, 26, 27, 28, 28, 29, 29, 30, 30, 31, 31, 32, 32, 33, 34, 34, 35, 35, 36, 36, 37, 37, 38, 38, 39, 39, 40, 41, 41

Offset

1,1

Comments

Least k such that Pochhammer(k, n) > n^n. - Ryan Propper, Sep 06 2005

Links

Table of n, a(n) for n=1..74.

Eric Weisstein's World of Mathematics, Pochhammer Symbol.

Formula

Limit_{n->oo} a(n)/n = A090462. - Ryan Propper, Sep 06 2005

Example

a(4) = 3: 2*3*4*5 = 120 < 256 = 4^4 < 3*4*5*6 = 360.

Mathematica

Do[k = 1; While[Pochhammer[k, n] <= n^n, k++ ]; Print[k], {n, 1, 100}] (* Ryan Propper, Sep 06 2005 *)

Prog

(PARI) b(n) = my(k=1); while(prod(i=k, k+n-1, i) <= n^n, k++); k; \\ Michel Marcus, Mar 08 2023

Crossrefs

Cf. A090462.

Sequence in context: A026830 A025155 A286744 * A025159 A373073 A264594

Adjacent sequences: A111681 A111682 A111683 * A111685 A111686 A111687

Keyword

nonn

Author

Amarnath Murthy, Aug 16 2005

Extensions

More terms from Ryan Propper, Sep 06 2005

Status

approved