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%I #26 Oct 27 2018 09:20:37
%S 251,1741,3301,5101,5381,6311,6361,12641,13451,14741,15791,15901,
%T 17471,18211,19471,23321,26171,30091,30631,53611,56081,62201,63691,
%U 71341,74453,75521,76543,77551,78791,80911,82781,83431,84431,89101,89381
%N First term of balanced prime quartets: p(m+1)-p(m) = p(m+2)-p(m+1) = p(m+3)-p(m+2).
%C This sequence is infinite if Dickson's conjecture holds. - _Charles R Greathouse IV_, Apr 23, 2011
%C This is actually the complete list of primes starting a CPAP-4 (set of 4 consecutive primes in arithmetic progression). It equals A033451 for a(1..24), but it contains a(25) = 74453 which starts a CPAP-4 with common difference 18 (the first one with a difference > 6) and therefore is not in A033451. - _M. F. Hasler_, Oct 26 2018
%H Zak Seidov and Charles R Greathouse IV, <a href="/A054800/b054800.txt">Table of n, a(n) for n = 1..10000</a> (first 4000 terms from Seidov)
%e a(1) = 251 = prime(54) = A000040(54) and prime(55) - prime(54) = prime(56)-prime(55) = 6. - _Zak Seidov_, Apr 23 2011
%t Select[Partition[Prime[Range[9000]],4,1],Length[Union[Differences[#]]] == 1&][[All,1]] (* _Harvey P. Dale_, Aug 08 2017 *)
%o (PARI) p=2;q=3;r=5;forprime(s=7,1e4, t=s-r; if(t==r-q&&t==q-p, print1(p", ")); p=q;q=r;r=s) \\ _Charles R Greathouse IV_, Feb 14 2013
%Y Cf. A006562, A054801 .. A054840.
%Y Cf. A006560 (first prime to start a CPAP-n).
%Y Start of CPAP-4 with given common difference (in square brackets): A033451 [6], A033447 [12], A033448 [18], A052242 [24], A052243 [30], A058252 [36], A058323 [42], A067388 [48], A259224 [54], A210683 [60].
%K nonn
%O 1,1
%A _Henry Bottomley_, Apr 10 2000
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