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%I #9 Dec 25 2020 19:33:33
%S 5,7,11,13,29,47,67,71,73,83,131,151,233,307,461,467,479,571,577,587,
%T 613,619,643,727,853,947,953,967,991,1063,1093,1231,1249,1291,1297,
%U 1427,1489,1493,1867,1871,1879,2017,2083,2111,2251,2309,2311,2473,2749,2753,2767,3011,3089,3191,3313,3691
%N Primes of the form (p + 2*q + r)/6 where p, q and r are consecutive primes.
%H Robert Israel, <a href="/A339953/b339953.txt">Table of n, a(n) for n = 1..10000</a>
%F a(n) = (A151799(A339954(n))+2*A339954(n)+A151800(A339954(n)))/6.
%e a(3) = 11 is a term because 13, 17, 19 are consecutive primes with (13+2*17+19)/6 = 11 and 11 is prime.
%p q:= 2: r:= 3:
%p count:= 0: R:= NULL:
%p while count < 100 do
%p p:= q; q:= r; r:= nextprime(r);
%p w:= (p+2*q+r)/6;
%p if w::integer and isprime(w) then
%p count:= count+1; R:= R, w;
%p fi
%p od:
%p R;
%Y Cf. A151799, A151800, A339954.
%K nonn
%O 1,1
%A _J. M. Bergot_ and _Robert Israel_, Dec 24 2020
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