A364845 a(n) is the denominator of the fraction h/k with h and k coprime palindrome positive integers at which abs(h/k-Pi) is minimal, with the numerator h of n digits.

1, 7, 151, 494, 11511, 93039, 2332332, 9966699

Offset

1,2

Comments

a(2) = 7 corresponds to the denominator of A068028.

Links

Table of n, a(n) for n=1..8.

Index entries for sequences related to the number Pi

Example

  n              fraction    approximated value
  -   -------------------    ------------------
  1                     3    3
  2                  22/7    3.1428571428571...
  3               474/151    3.1390728476821...
  4              1551/494    3.1396761133603...
  5           36163/11511    3.1416036834332...
  6          292292/93039    3.1416072829673...
  7       7327237/2332332    3.1415926206046...
  8      31311313/9966699    3.1415931192464...
  ...

Mathematica

nmax = 8; a = {1}; hmin = kmin = 0; For[n = 2, n <= nmax, n++, minim = Infinity; h = Select[Range[10^(n - 1), 10^n - 1], PalindromeQ]; k = Select[Range[10^(n - 2), 10^n - 1], PalindromeQ]; lh = Length[h]; lk = Length[k];  For[i = 1, i <= lh, i++, For[j = 1, j <= lk, j++, If[(dist = Abs[Part[h, i]/Part[k, j] - Pi]) < minim && GCD[Part[h, i], Part[k, j]] == 1, minim = dist; kmin = Part[k, j]]]]; AppendTo[a, kmin]]; a

Crossrefs

Cf. A000796, A002113, A068028, A070252, A364844 (numerator), A364846.

Cf. A355622, A355623.

Sequence in context: A070248 A329010 A309855 * A339582 A232446 A362491

Adjacent sequences: A364842 A364843 A364844 * A364846 A364847 A364848

Keyword

nonn,base,frac,more

Author

Stefano Spezia, Aug 10 2023

Status

approved