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Primes, q, such that for three consecutive primes, p, q & r, with p<q<r, (q - p)/(r - q) is an integer.

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`%I #9 Jul 26 2018 15:05:53
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`%S 5,11,17,29,41,53,59,71,97,101,107,137,149,157,173,179,191,197,211,
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`%T 223,227,239,257,263,269,281,311,347,373,397,419,431,457,461,487,499,
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`%U 521,541,563,569,593,599,607,617,641,653,659,673,733,769,809,821,827,857
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`%N Primes, q, such that for three consecutive primes, p, q & r, with p<q<r, (q - p)/(r - q) is an integer.
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`%C The distance between the cited prime above to its immediate predecessor is divisible by the distance from that prime to its immediate successor.
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`%C Intersection(A184247, A184248): 5, 53, 157, 173, 211, ..., = A006562: Balanced primes (of order 1).
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`%H Harvey P. Dale, <a href="/A184247/b184247.txt">Table of n, a(n) for n = 1..1000</a>
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`%t fQ[n_] := Block[{p = NextPrime[n, -1], q = n, r = NextPrime[n]}, IntegerQ[(q - p)/(r - q)]]; Select[ Prime@ Range[2, 50], fQ]
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`%t Select[Partition[Prime[Range[150]],3,1],IntegerQ[(#[[2]]-#[[1]])/(#[[3]]- #[[2]])]&][[All,2]] (* _Harvey P. Dale_, Jul 26 2018 *)
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`%Y Cf. A184248.
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`%K easy,nonn
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`%O 1,1
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`%A _Robert G. Wilson v_, Jan 10 2011
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