A217314 Smallest k such that k! > A000178(n) (the superfactorials).

2, 2, 3, 4, 6, 8, 11, 15, 18, 23, 27, 33, 38, 44, 51, 58, 65, 73, 81, 90, 100, 109, 120, 130, 141, 153, 165, 178, 191, 204, 218, 233, 247, 263, 279, 295, 312, 329, 347, 365, 383, 402, 422, 442, 462, 483, 505, 527, 549, 572, 595, 619, 643, 668, 693, 719, 745

Offset

0,1

Links

Table of n, a(n) for n=0..56.

Eric W. Weisstein, Mathworld: Factorial

Eric W. Weisstein, Mathworld: Superfactorial

Wikipedia, Factorial

Example

SF(4) = 4!*3!*2!*1! = 288, and 5! < 288 < 6! so a(4)=6.

Mathematica

a[n_] := Block[{ff = Product[k!, {k, n}], k = 1}, While[k! <= ff, k++]; k]; Table[a[n], {n, 0, 60}] (* Giovanni Resta, Mar 18 2013 *)

Prog

(JavaScript)
function factorial(n) {
var i, c=1;
for (i=2; i<=n; i++) c*=i;
return c;
}
k=1;
m=1;
for (i=2; i<30; i++) {
k*=factorial(i);
while (factorial(m)<=k) m++;
document.write(m+", ");
}

Crossrefs

Cf. A000142, A000178.

Sequence in context: A182372 A089333 A098492 * A173508 A103632 A214076

Adjacent sequences: A217311 A217312 A217313 * A217315 A217316 A217317

Keyword

nonn

Author

Jon Perry, Mar 17 2013

Extensions

a(27)-a(56) from Giovanni Resta, Mar 18 2013

Status

approved