The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A216761 n * floor(log_2(n)) * floor(log_2(log_2(n))) * floor(log_2(log_2(log_2(n)))) .... 2
 1, 2, 3, 8, 10, 12, 14, 24, 27, 30, 33, 36, 39, 42, 45, 128, 136, 144, 152, 160, 168, 176, 184, 192, 200, 208, 216, 224, 232, 240, 248, 320, 330, 340, 350, 360, 370, 380, 390, 400, 410, 420, 430, 440, 450, 460, 470, 480, 490, 500, 510, 520, 530, 540, 550 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) is the product of n, floor(log_2 n), floor (log_2(log_2 n)), ... with the base-2 logs iterated while the result remains greater than unity. The sum of the reciprocals of a(n) diverge, but extremely slowly. In particular, the sum of the reciprocals acts like lg* n asymptotically, where lg* x = 0 for x < 2 and lg* 2^x = 1 + lg* x. - Charles R Greathouse IV, Sep 25 2012 LINKS EXAMPLE a(0) is the product of 0 numbers, defined to be 1. a(15) = 15 * floor(log_2 15) * floor(log_2 log_2 15) = 15 * 3 * 1 = 45. a(17) = 17 * floor(log_2 17) * floor(log_2 log_2 17) * floor(log_2 log_2 log_2 17) = 17 * 4 * 2 * 1 = 136. MATHEMATICA Table[prod = 1; s = n; While[s > 1, prod = prod*Floor[s]; s = Log[2, s]]; prod, {n, 60}] (* T. D. Noe, Sep 24 2012 *) PROG (Haskell) a = product . map floor . takeWhile (1<) . iterate log_2 (PARI) a(n)=my(t=n); n+=1e-9; while(n>2, t*=floor(n=log(n)/log(2))); t \\ Charles R Greathouse IV, Sep 25 2012 CROSSREFS Cf. A216762 (ceiling instead of floor). Sequence in context: A190650 A000059 A340301 * A276559 A097053 A190668 Adjacent sequences:  A216758 A216759 A216760 * A216762 A216763 A216764 KEYWORD nonn AUTHOR Ken Takusagawa, Sep 15 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified June 19 21:04 EDT 2021. Contains 345147 sequences. (Running on oeis4.)