A051889 a(n) = min{m: Sum_{j=0..m} binomial(n,j)*(1/6)^j*(1-1/6)^(n-i) >= 0.95}.

0, 1, 1, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5, 5, 5, 5, 6, 6, 6, 6, 6, 7, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 11, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13, 14, 14, 14, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 16, 17, 17, 17, 17, 17, 18, 18, 18, 18, 18, 19, 19, 19

Offset

0,4

Comments

If you toss an idealized (six-sided) die n times, then the probability of obtaining more than a(n) 6's is <= 5 percent.

Links

Table of n, a(n) for n=0..80.

Mathematica

s[m_, n_] := Sum[Binomial[n, i]*(1/6)^i*(1 - 1/6)^(n - i), {i, 0, m}]; a[0] = 0; a[n_] := a[n] = For[m = a[n - 1], True, m++, If[s[m, n] >= 95/100, Return[m]]]; Table[a[n], {n, 0, 80}] (* Jean-François Alcover, Oct 11 2012 *)

Crossrefs

Cf. A039708 (similar for a coin).

Sequence in context: A076885 A274024 A285189 * A086707 A217538 A333348

Adjacent sequences: A051886 A051887 A051888 * A051890 A051891 A051892

Keyword

easy,nice,nonn

Author

Klaus Strassburger (strass(AT)ddfi.uni-duesseldorf.de), Dec 15 1999

Status

approved