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%I #3 Sep 08 2022 08:45:30
%S 397,1277,2939,4217,10211,11657,13049,17117,17791,19507,23117,25913,
%T 31259,36523,42677,44777,45659,49711,54499,56701,63521,64283,73877,
%U 74573,85093,88609,89477,89759,90059,93563,104161,104831,106937,108179
%N Primes q such that p = (r+q+s-1)/2 is a balanced prime, where r, q, s are consecutive primes.
%C The primes p arising here are in A129191.
%C q need not be a balanced prime, see however A129241.
%e 389, 397, 401 are consecutive primes. 593 = (389+397+401-1)/2 = A006562(10) is a balanced prime, it is the average of the preceding prime 587 and the next prime 599. Hence 397 is a term.
%o (Magma) [ q: q in PrimesInInterval(3, 110000) | IsPrime(p) and PreviousPrime(p)+NextPrime(p) eq 2*p where p is (PreviousPrime(q)+q+NextPrime(q)-1) div 2 ];
%Y Cf. A006562 (balanced primes), A127313, A129191, A129241.
%K nonn
%O 1,1
%A _Klaus Brockhaus_, Apr 05 2007
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