OFFSET
1,1
COMMENTS
Not every three successive primes have an integer average. The integer averages are in A075540.
Not all of these 3-averages are prime: the prime 3-averages are in A006562 (balanced primes). There are surprisingly many prime 3-averages: among first 117 3-averages, there are 59 primes. Indices i(n) of first prime in sequence of three primes with integer average are in sequence A064113. Interprimes (s-averages with s=2) are all composite, see A024675.
FORMULA
i(n)-> 1/3 (p(i)+p(i+1)+p(i+2)) is integer.
EXAMPLE
i(2) = 15 because (p(15)+p(16)+p(17)) = 1/3(47 + 53 + 59)=53 (integer average of three successive primes).
MATHEMATICA
CROSSREFS
KEYWORD
nonn
AUTHOR
Zak Seidov, Sep 21 2002
STATUS
approved