A178851 - OEIS

%I #10 Jan 20 2014 22:13:30

%S 0,0,1,7,32,121,412,1317,4048,12144,35904,105249,306968,892217,

%T 2585468,7468532,21500800,61688513,176477988,503906221,1438235592,

%U 4110846808,11789919200,33991337521,98657320240,288505634480,850146795840,2522918119392,7531922736384

%N The number of length n sequences on {0,1,2}(ternary sequences) that contain a prime number of 2's.

%C a(n) is the number of positive integers less than 3^n that when expressed as a ternary numeral contain a prime number of 2's.

%C a(n)/3^n is the probability that a series of Bernoulli trials with probability of success equal to 1/3 will result in a prime number of successes. Cf. A121497

%H Eric M. Schmidt, <a href="/A178851/b178851.txt">Table of n, a(n) for n = 0..2000</a>

%F E.g.f.:exp(2x)*(x^2/2!+x^3/3!+x^5/5!+...)

%F a(n) = Sum Binomial(n,p)*2^(n-p) where the sum is taken over the prime numbers.

%e a(3)=7 because 8,17,20,23,24,25,26 have a prime number of 2's in their ternary notation.

%t P=Table[Prime[m],{m,1,200}];Range[0,20]! CoefficientList[Series[Exp[2x] Sum[x^p/p!,{p,P}],{x,0,20}],x]

%K nonn

%O 0,4

%A _Geoffrey Critzer_, Dec 27 2010