A286742 a(n) minimizes (over the integers) the absolute difference between Pi and x(n) + 1/a(n), where x(n) is Pi truncated at the n-th decimal digit.

7, 24, 628, 1687, 10793, 376848, 1530012, 18660270, 278567575, 1695509434, 11136696004, 102111268282, 1260654956982, 10725187563686, 308788493220130, 4193528956200936, 25999253094360135, 118166387818704585, 2161492060929047665, 15963377896404315144

Offset

1,1

Links

Table of n, a(n) for n=1..20.

Example

3 + 1/7 is closest to Pi in absolute value among numbers of the form 3 + 1/k (k an integer); 3.1 + 1/24 is closest to Pi in absolute value among numbers of the form 3.1 + 1/k (k an integer); 3.14 + 1/628 is closest to Pi in absolute value among numbers of the form 3.14 + 1/k (k an integer).

Mathematica

Table[
   truncpi = Floor[10^(n - 1)*Pi]/10^(n - 1);
    SortBy[
      {Floor[1/(Pi - truncpi)], Ceiling[1/(Pi - truncpi)]},
      N[Abs[Pi - (truncpi + 1/#)]] &
   ][[1]],
{n, 1, 20}] (* first 20 terms *)

Crossrefs

Cf. A074783.

Sequence in context: A009652 A012777 A074783 * A322563 A065658 A242322

Adjacent sequences: A286739 A286740 A286741 * A286743 A286744 A286745

Keyword

nonn,base

Author

Jason Zimba, May 13 2017

Status

approved