This site is supported by donations to The OEIS Foundation.

 Please make a donation to keep the OEIS running. We are now in our 55th year. In the past year we added 12000 new sequences and reached 8000 citations (which often say "discovered thanks to the OEIS"). We need to raise money to hire someone to manage submissions, which would reduce the load on our editors and speed up editing. Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A248103 Least k such that ((2k+1)/(2k-1))^k < 1/(2n^2). 3
 1, 2, 3, 3, 4, 5, 5, 6, 7, 7, 8, 9, 9, 10, 11, 11, 12, 13, 13, 14, 15, 15, 16, 17, 17, 18, 19, 19, 20, 21, 21, 22, 23, 23, 24, 25, 25, 26, 27, 27, 28, 29, 29, 30, 31, 31, 32, 33, 33, 34, 35, 36, 36, 37, 38, 38, 39, 40, 40, 41, 42, 42, 43, 44, 44, 45, 46, 46 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS In general, for fixed positive m, the limit of ((m*x+1)/(m*x-1))^x is e^(2/m), as illustrated by A248103, A248106, A248111. REFERENCES Steven R. Finch, Mathematical Constants, Cambridge University Press, 2003, p. 14. LINKS Clark Kimberling, Table of n, a(n) for n = 1..1000 EXAMPLE Approximations are shown here: n ... ((2n+1)/(2n-1))^n ... 1/(2*n^2) 1 ... 0.281718 ............ 0.5 2 ... 0.0595959 ........... 0.125 3 ... 0.0257182 ........... 0.05555 4 ... 0.0143296 ........... 0.3125 a(4) = 3 because p(4) - e < 1/32 < p(3) - e. MATHEMATICA z = 1200; p[k_] := p[k] = ((2 k + 1)/(2 k - 1))^k; N[Table[p[n] - E, {n, 1, z/8}]] f[n_] := f[n] = Select[Range[z], p[#] - E < 1/(2 n^2) &, 1] u = Flatten[Table[f[n], {n, 1, z/10}]]  (* A248103 *) CROSSREFS Cf. A248106, A248111. Sequence in context: A131737 A004396 A066481 * A121928 A175406 A210435 Adjacent sequences:  A248100 A248101 A248102 * A248104 A248105 A248106 KEYWORD nonn,easy AUTHOR Clark Kimberling, Oct 02 2014 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 December 14 12:04 EST 2019. Contains 329979 sequences. (Running on oeis4.)