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 A084321 Least number k such that between k! and (k+1)! there are n powers of 2. 3
 1, 3, 5, 10, 19, 35, 64, 139, 256, 536, 1061, 2095, 4169, 8282, 16517, 32903, 65646, 131205, 262579, 525083, 1048893, 2098826, 4195521, 8390583, 16782032, 33569609, 67118347, 134229613, 268453180, 536890474, 1073764782, 2147523518 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is near the (n-1)th power of 2, the difference is A085355. LINKS FORMULA a(n)=Min{x; Floor[Log[2, (x+1)! ]]-Floor[Log[2, x! ]]=n}= Min{x; A084320(x)=n}. EXAMPLE a(3)=5 since between 5!=120 and 6!=720 is the first time 3 powers of 2 arise, namely, 128, 256 and 512. MATHEMATICA LogBase2Stirling[n_] := N[ Log[2, 2 Pi n]/2 + n*Log[2, n/E] + Log[2, 1 + 1/(12n) + 1/(288n^2) - 139/(51840n^3) - 571/(2488320n^4) + 163879/(209018880n^5)], 64]; k = 1; Do[ While[ Floor[ LogBase2Stirling[k + 1]] - Floor[ LogBase2Stirling[k]] < n, k++ ]; Print[k], {n, 1, 33}] CROSSREFS Cf. A067850, A058033, A000142, A000079, A084320. Sequence in context: A125750 A018168 A320921 * A323812 A270715 A291735 Adjacent sequences:  A084318 A084319 A084320 * A084322 A084323 A084324 KEYWORD nonn AUTHOR Labos Elemer, Jun 19 2003 EXTENSIONS Edited and extended by Robert G. Wilson v, Jun 24 2003 STATUS approved

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Last modified October 21 01:08 EDT 2019. Contains 328291 sequences. (Running on oeis4.)