A084420 Least number k such that between k! and (k+1)! there are n powers of ten.

3, 14, 103, 1042, 10158, 100502, 1000617, 10006509, 100019088, 1000004377, 10000170793, 100000442970, 1000001981666, 10000005339905

Offset

1,1

Comments

a(15)>100000018000000.

Links

Table of n, a(n) for n=1..14.

Mathematica

LogBase10Stirling[n_] := Floor[ Log[10, 2 Pi n]/2 + n * Log[10, n/E] + Log[10, 1 + 1/(12n) + 1/(288n^2) - 139/(51840n^3) - 571/(2488320n^4) + 163879/(209018880n^5)]]; Do[k = 10^(n - 1); While[ LogBase10Stirling[k + 1] - LogBase10Stirling[k] < n, k++ ]; a[n] = k; Print[ a[n]], {n, 1, 14}]

Crossrefs

Cf. A084321.

Sequence in context: A076015 A004659 A054202 * A163882 A271213 A167017

Adjacent sequences: A084417 A084418 A084419 * A084421 A084422 A084423

Keyword

nonn

Author

Robert G. Wilson v, Jun 26 2003

Status

approved