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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.
5
1, 4, 323, 939, 14341, 61716, 1621261, 9192919, 324707423, 509838905, 30546664503, 59359795395, 3329737379233, 9164547454619
OFFSET
1,2
COMMENTS
a(3) = 323 corresponds to the denominator of A368617.
EXAMPLE
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...
...
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]
PROG
(PARI) \\ See PARI program in Links
CROSSREFS
Cf. A364845 (similar for Pi), A368620, A368621.
Sequence in context: A034226 A186163 A159492 * A368369 A053917 A005832
KEYWORD
nonn,base,frac,more
AUTHOR
Stefano Spezia, Jan 01 2024
EXTENSIONS
a(10)-a(14) from David A. Corneth, Jan 03 2024
STATUS
approved