A368618 a(n) is the n-digit numerator of the fraction h/k with h and k coprime palindrome positive integers at which abs(h/k-e) is minimal.
3, 11, 878, 2552, 38983, 167761, 4407044, 24988942, 882646288, 1385885831, 83034443038, 161356653161, 9051164611509, 24911822811942
Offset: 1
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
Programs
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Mathematica
a[1]=3; 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; hmin = Part[h, i]]]]; hmin]; Array[a,9] -
PARI
\\ See PARI program in Links
Extensions
a(10)-a(14) from David A. Corneth, Jan 03 2024
Comments