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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, 100000018997256, 1000000065392525, 10000000201014294, 100000000631520633, 1000000001077349719, 10000000005309690910

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OFFSET

1,1

LINKS

Kevin Ryde, Table of n, a(n) for n = 1..400

Kevin Ryde, C code.

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}]

PROG

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

EXTENSIONS

a(15)-a(20) from Kevin Ryde, Mar 09 2024

STATUS

approved

URL: https://oeis.org/A084420

⇱ A084420 - OEIS