This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
(r - q)/(q - p) is an integer.
%I A184248 #9 Mar 30 2014 14:16:53 %S A184248 3,5,7,13,19,31,43,53,61,73,103,109,139,151,157,173,181,193,199,211, %T A184248 229,241,257,263,271,283,313,349,373,401,421,433,463,467,491,509,523, %U A184248 563,571,593,601,607,619,643,653,661,733,743,761,811,823,829,859 %N A184248 Primes, q, such that for three consecutive primes, p, q & r, with p<q<r, (r - q)/(q - p) is an integer. %C A184248 The distance between the cited prime above to its immediate successor is divisible by the distance from that prime to its immediate predecessor. %C A184248 Intersection(A184247, A184248): 5, 53, 157, 173, 211, .., = A006562: Balanced primes (of order 1). %H A184248 Harvey P. Dale, <a href="/A184248/b184248.txt">Table of n, a(n) for n = 1..1000</a> %t A184248 fQ[n_] := Block[{p = NextPrime[n, -1], q = n, r = NextPrime[n]}, IntegerQ[(r - q)/(q - p)]]; Select[ Prime@ Range@ 150, fQ] %t A184248 Transpose[Select[Partition[Prime[Range[200]],3,1],IntegerQ[(#[[3]]- #[[2]])/ (#[[2]]-#[[1]])]&]][[2]] (* _Harvey P. Dale_, Mar 30 2014 *) %Y A184248 Cf. A184247. %K A184248 easy,nonn %O A184248 1,1 %A A184248 _Robert G. Wilson v_, Jan 10 2011