OFFSET
0,4
COMMENTS
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.
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
LINKS
Eric M. Schmidt, Table of n, a(n) for n = 0..2000
FORMULA
E.g.f.:exp(2x)*(x^2/2!+x^3/3!+x^5/5!+...)
a(n) = Sum Binomial(n,p)*2^(n-p) where the sum is taken over the prime numbers.
EXAMPLE
a(3)=7 because 8,17,20,23,24,25,26 have a prime number of 2's in their ternary notation.
MATHEMATICA
P=Table[Prime[m], {m, 1, 200}]; Range[0, 20]! CoefficientList[Series[Exp[2x] Sum[x^p/p!, {p, P}], {x, 0, 20}], x]
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Dec 27 2010
STATUS
approved