A368619 a(n) is the n-digit denominator of the fraction h/k with h and k coprime palindrome positive integers at which abs(h/k-e) is minimal.

1, 4, 323, 939, 14341, 61716, 1621261, 9192919, 324707423, 509838905, 30546664503, 59359795395, 3329737379233, 9164547454619

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                  11/4    2.75
  3               878/323    2.7182662538699...
  4              2552/939    2.7177848775292...
  5           38983/14341    2.7182902168607...
  6          167761/61716    2.7182740294251...
  7       4407044/1621261    2.7182816338640...
  8      24988942/9192919    2.7182815382143...
  9   882646288/324707423    2.7182818299783...
  ...
		

Links

• David A. Corneth, PARI program
• Index entries for sequences related to the number e

Crossrefs

Cf. A001113, A002113, A070252, A368617, A368618 (numerator), A368658.

Cf. A007676, A007677.

Cf. A364845 (similar for Pi), A368620, A368621.

Programs

Mathematica

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

PARI

\\ See PARI program in Links

Extensions

a(10)-a(14) from David A. Corneth, Jan 03 2024