A100332 a(n) is the smallest positive integer for which the fractional part of exp(a(n)) begins with n.

11, 14, 2, 5, 4, 7, 1, 24, 8, 363, 61, 140, 18, 11, 56, 281, 204, 81, 391, 624, 154, 36, 173, 23, 98, 63, 181, 14, 139, 37, 60, 82, 153, 519, 54, 315, 15, 2, 13, 20, 5, 6, 67, 297, 50, 10, 28, 21, 118, 115, 172, 16, 487, 272, 55, 93, 258, 249, 4, 99, 87, 282, 7, 73, 134, 242

Offset: 1

Author

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 17 2004

Keywords

• base
• nonn

Examples

			a(1)=11 because exp(11)=59874.1... and no other 1<= k < 11 gives (exp(k)) whose fractional part starts with 1;
a(2)=14 because exp(14)=1202604.2...;
a(7)=1 because exp(1)=2.7...;
		

Links

• Robert Israel, Table of n, a(n) for n = 1..3908

Crossrefs

Cf. A100322 for analogous sequence for Pi.

Programs

Maple

V:= Array(0..999):
count:= 0:
for n from 1 while count < 999 do
  d:= floor(log10(exp(n)));
  Digits:= d+10;
  for m from 1 to 3 do
    x:= floor(10^m*exp(n)) mod 10^m;
    if x >= 10^(m-1) and V[x] = 0 then
      count:= count+1;
      V[x]:= n
    fi
  od;
od:
seq(V[i],i=1..999); # Robert Israel, Dec 14 2015