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 A084420 Least number k such that between k! and (k+1)! there are n powers of ten. 2
 3, 14, 103, 1042, 10158, 100502, 1000617, 10006509, 100019088, 1000004377, 10000170793, 100000442970, 1000001981666, 10000005339905, 100000018997256, 1000000065392525, 10000000201014294, 100000000631520633, 1000000001077349719, 10000000005309690910 (list; graph; refs; listen; history; text; internal format)
 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 (C) /* See links. */ 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

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Last modified May 24 12:09 EDT 2024. Contains 372773 sequences. (Running on oeis4.)