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 A085355 a(n) is the difference between A084321(n) and the (n-1)th power of 2. 3
 0, 1, 1, 2, 3, 3, 0, 11, 0, 24, 37, 47, 73, 90, 133, 135, 110, 133, 435, 795, 317, 1674, 1217, 1975, 4816, 6177, 9483, 11885, 17724, 19562, 22958, 39870, 48417, 85452, 114676, 210482, 133092, 194048, 524165, 451743, 1145779, 1292884, 1604772, 2859433, 4032594 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,4 COMMENTS A084321 is the least number k such that between k! and (k+1)! there are n powers of 2. LINKS Kevin Ryde, Table of n, a(n) for n = 1..1000 MATHEMATICA LogBase2Stirling[n_] := Floor[ 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)]]; Do[k = 2^(n - 1); While[ LogBase2Stirling[k + 1] - LogBase2Stirling[k] < n, k++ ]; a[n] = k, {n, 1, 45}]; Table[ a[n] - 2^(n - 1), {n, 1, 45}] CROSSREFS Cf. A084321. Sequence in context: A329232 A057682 A124841 * A103120 A021433 A228624 Adjacent sequences: A085352 A085353 A085354 * A085356 A085357 A085358 KEYWORD nonn AUTHOR Labos Elemer and Robert G. Wilson v, Jun 24 2003 STATUS approved

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Last modified May 28 19:55 EDT 2024. Contains 372919 sequences. (Running on oeis4.)