A178851 The number of length n sequences on {0,1,2}(ternary sequences) that contain a prime number of 2's.

0, 0, 1, 7, 32, 121, 412, 1317, 4048, 12144, 35904, 105249, 306968, 892217, 2585468, 7468532, 21500800, 61688513, 176477988, 503906221, 1438235592, 4110846808, 11789919200, 33991337521, 98657320240, 288505634480, 850146795840, 2522918119392, 7531922736384

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

Sequence in context: A001794 A140289 A133107 * A213163 A249999 A034360

Adjacent sequences: A178848 A178849 A178850 * A178852 A178853 A178854

Keyword

nonn

Author

Geoffrey Critzer, Dec 27 2010

Status

approved