A100322 -id:A100322 - cp's OEIS frontend

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

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

			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...;

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

Cf. A100322 for analogous sequence for Pi.

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

A100323 Numbers k such that the decimal expansion of Pi^k begins (after the decimal point) with k.

Original entry on oeis.org

1, 4, 75, 9424, 12669, 331783

Offset: 1

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 16 2004

The terms of this sequence are related to those in A100322, but do not necessarily appear in that sequence since A100322(n) is defined as the smallest positive integer k such that the digits of the fractional part of Pi^k begin with n.

			Pi^1 = 3.1...;
Pi^4 = 97.4...;
Pi^75 = 19330382693312372796273669213182810875.75...

Cf. A100322.

p = N[Pi, 10^4]; f[n_] := Block[{r = RealDigits[p^n, 10, Max[5, n]]}, e = r[[2]]; FromDigits[ Take[r[[1]], {e + 1, e + 1 + Floor[ Log[10, n]]} ]]]; Do[ If[ f[n] == n, Print[n]], {n, 10^4}] (* Robert G. Wilson v, Nov 16 2004 *)

a(6) from Jon E. Schoenfield, Mar 28 2015

A100333 Numbers n such that decimal expansion of exp(n) has fractional part beginning with n.

Original entry on oeis.org

40, 55, 71, 5833

Offset: 1

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 18 2004

This sequence (like A100323 relative to A100322) is not necessarily a subset of A100332 because there may exist an n1A100332.

			E.g. exp(40)=235385266837019985.40...
exp(55)=769478526514201713818274.55...
exp(71)=6837671229762743866755892826677.71... etc

Cf. A100323 for analogous sequence relating to powers of Pi.

cp's OEIS Frontend

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

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A100323 Numbers k such that the decimal expansion of Pi^k begins (after the decimal point) with k.

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A100333 Numbers n such that decimal expansion of exp(n) has fractional part beginning with n.

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