A368621 a(n) is the n-digit denominator of the fraction h/k with h and k coprime positive integers at which abs(h/k-e) is minimal.

1, 32, 323, 1001, 18089, 208524, 3400196, 10391023, 312129649

Offset: 1

Author

Stefano Spezia, Jan 01 2024

Keywords

• nonn
• base
• frac
• more

Comments

a(3) = 323 corresponds to the denominator of A368617.

Examples

			  n              fraction    approximated value
  -   -------------------    ------------------
  1                   3/1    3
  2                 87/32    2.71875
  3               878/323    2.7182662538699...
  4             2721/1001    2.7182817182817...
  5           49171/18089    2.7182818287356...
  6         566827/208524    2.7182818284705...
  7       9242691/3400196    2.7182818284593...
  8     28245729/10391023    2.7182818284590...
  ...
		

Links

• Index entries for sequences related to the number e

Crossrefs

Cf. A001113, A368617, A368620 (numerator), A368659.

Cf. A007676, A007677, A368618, A368619.

Programs

Mathematica

a[1]=1; a[n_]:=Module[{minim=Infinity},For[i = 10^(n - 1), i <= 10^n - 1, i++, For[j = Floor[i/E], j <= Ceiling[i/E], j++, If[(dist = Abs[i/j - E]) < minim && GCD[i, j] == 1, minim = dist; kmin = j]]]; kmin]; Array[a,9]