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%I #12 Jun 08 2015 10:35:30
%S 0,1,1,3,6,7,11,15,16,25,30,32,42,40,44,52,63,71,76,87,82,97,102,113,
%T 127,137,136,143,154,154,186,200,204,215,234,249,251,262,272,284,309,
%U 324,345,334,349,359,406,414,431,447,441,489,487,511,508
%N Number of ways to represent the n-th prime as arithmetic mean of three other primes.
%C Differs from A071704: for n>1, if 3*prime(n)-4 is prime then a(n)=1+A071704(n), otherwise a(n)=A071704(n).
%H Zak Seidov and Charles R Greathouse IV, <a href="/A258233/b258233.txt">Table of n, a(n) for n = 1..10000</a> (first 1000 terms from Seidov)
%e a(5)=6 as A000040(5)=11 and 11 has 6 representations as arithmetic mean of three other (not equal to 11) primes:
%e 11 = (2+2+29)/3=(3+7+23)/3 = (3+13+17)/3 = (5+5+23)/3 = (7+7+19)/3 = (7+13+13)/3.
%o (PARI) a(n,p=prime(n))=my(s=0); forprime(q=p+2,3*p-4, my(t=3*p-q); forprime(r=max(t-q, 2),(3*p-q)\2, if(t!=p+r && isprime(t-r), s++))); s \\ _Charles R Greathouse IV_, Jun 04 2015
%Y Cf. A000040, A071703, A071704.
%K nonn
%O 1,4
%A _Zak Seidov_, May 24 2015