%I #8 Oct 20 2016 12:05:51
%S 23,37,47,67,79,83,89,113,127,131,163,167,233,251,277,293,307,317,331,
%T 337,353,359,367,379,383,389,409,439,443,449,479,503,547,557,577,587,
%U 613,631,647,677,683,691,701,709,719,727,739,751,757,773,787,797,839,853,863
%N Primes, q, such that for three consecutive primes, p, q & r, with p<q<r, neither (q - p)/(r - q) nor (r - q)/(q - p) is an integer.
%C The distance between the cited prime above to its immediate predecessor and the distance from that prime to its immediate successor is a ratio a/b with neither a nor b equal to 1.
%C Complement(A000040, A184247 & A184248)
%H Harvey P. Dale, <a href="/A179780/b179780.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[(q - p)/(r - q)] && !IntegerQ[(r - q)/(q - p)]]; Select[ Prime@ Range@ 150, fQ]
%t Select[Partition[Prime[Range[200]],3,1],NoneTrue[{(#[[2]]-#[[1]])/ (#[[3]]- #[[2]]),(#[[3]]-#[[2]])/(#[[2]]-#[[1]])},IntegerQ]&][[All,2]] (* Requires Mathematica version 10 or later *) (* _Harvey P. Dale_, Oct 20 2016 *)
%Y Cf. A184247 & A184248.
%K easy,nonn
%O 1,1
%A _Robert G. Wilson v_, Jan 10 2011