%I #9 Mar 30 2014 14:16:53
%S 3,5,7,13,19,31,43,53,61,73,103,109,139,151,157,173,181,193,199,211,
%T 229,241,257,263,271,283,313,349,373,401,421,433,463,467,491,509,523,
%U 563,571,593,601,607,619,643,653,661,733,743,761,811,823,829,859
%N Primes, q, such that for three consecutive primes, p, q & r, with p<q<r, (r - q)/(q - p) is an integer.
%C The distance between the cited prime above to its immediate successor is divisible by the distance from that prime to its immediate predecessor.
%C Intersection(A184247, A184248): 5, 53, 157, 173, 211, .., = A006562: Balanced primes (of order 1).
%H Harvey P. Dale, <a href="/A184248/b184248.txt">Table of n, a(n) for n = 1..1000</a>
%t fQ[n_] := Block[{p = NextPrime[n, -1], q = n, r = NextPrime[n]}, IntegerQ[(r - q)/(q - p)]]; Select[ Prime@ Range@ 150, fQ]
%t Transpose[Select[Partition[Prime[Range[200]],3,1],IntegerQ[(#[[3]]- #[[2]])/ (#[[2]]-#[[1]])]&]][[2]] (* _Harvey P. Dale_, Mar 30 2014 *)
%Y Cf. A184247.
%K easy,nonn
%O 1,1
%A _Robert G. Wilson v_, Jan 10 2011