A306975 Numbers n>1 such that the difference between log(n) and its best rational approximation as x/y with y<=n produces a new minimum of abs(log(n)-x/y). x/y is provided as A306976/A306977.

2, 3, 4, 5, 6, 9, 10, 11, 17, 19, 60, 66, 89, 576, 3069, 3901, 6270, 7542, 13046, 13215, 27952, 43110, 46605, 55413, 61421, 93159, 96004, 164035, 248150, 298207, 301985, 749378, 1149838, 1948414, 1959239, 2045876, 2174103, 2819116, 3666855, 3935292, 4650787, 4746097

Offset

1,1

Links

Table of n, a(n) for n=1..42.

Example

   k  L=log(k)     x/y  |L - x/y|
   2 0.6931471...  1/2  0.1931471... new minimum
   3 1.0986122...  1/1  0.0986122... new minimum
   4 1.3862943...  4/3  0.0529610... new minimum
   5 1.6094379...  8/5  0.0094379... new minimum
   6 1.7917594...  9/5  0.0082405... new minimum
   7 1.9459101...  2/1  0.0540898...
   8 2.0794415... 17/8  0.0455584...
   9 2.1972245... 11/5  0.0027754... new minimum
  10 2.3025850... 23/10 0.0025850... new minimum
  11 2.3978952... 12/5  0.0021047... new minimum
  12 2.4849066...  5/2  0.0150933...
  13 2.5649493... 18/7  0.0064792...
  14 2.6390573... 29/11 0.0026936...
  15 2.7080502... 19/7  0.0062355...
  16 2.7725887... 36/13 0.0033579...
  17 2.8332133... 17/6  0.0001199... new minimum
.
  a(1..9)       = [2, 3, 4, 5, 6,  9, 10, 11, 17],
  A306976(1..9) = [1, 1, 4, 8, 9, 11, 23, 12, 17],
  A306977(1..9) = [2, 1, 3, 5, 5,  5, 10,  5,  6].

Prog

(PARI) dmin=1; for(k=2, 5000000, L=log(k); d=abs(L-bestappr(L, k)); if(d<dmin, dmin=d; print1(k, ", ")))

Crossrefs

Cf. A306972, A306976, A306977.

Sequence in context: A137582 A116965 A356007 * A123054 A093703 A117073

Adjacent sequences: A306972 A306973 A306974 * A306976 A306977 A306978

Keyword

nonn

Author

Hugo Pfoertner, Mar 18 2019

Status

approved