A085355 a(n) is the difference between A084321(n) and the (n-1)th power of 2.

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

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