A054800 First term of balanced prime quartets: p(m+1)-p(m) = p(m+2)-p(m+1) = p(m+3)-p(m+2).

251, 1741, 3301, 5101, 5381, 6311, 6361, 12641, 13451, 14741, 15791, 15901, 17471, 18211, 19471, 23321, 26171, 30091, 30631, 53611, 56081, 62201, 63691, 71341, 74453, 75521, 76543, 77551, 78791, 80911, 82781, 83431, 84431, 89101, 89381

Offset: 1

Author

Henry Bottomley, Apr 10 2000

Keywords

• nonn

Comments

This sequence is infinite if Dickson's conjecture holds. - Charles R Greathouse IV, Apr 23 2011

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

Examples

			a(1) = 251 = prime(54) = A000040(54) and prime(55) - prime(54) = prime(56)-prime(55) = 6. - _Zak Seidov_, Apr 23 2011
		

Links

• Zak Seidov and Charles R Greathouse IV, Table of n, a(n) for n = 1..10000 (first 4000 terms from Seidov)

Crossrefs

Cf. A006562, A054801 .. A054840.

Cf. A006560 (first prime to start a CPAP-n).

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].

Programs

Mathematica

Select[Partition[Prime[Range[9000]],4,1],Length[Union[Differences[#]]] == 1&][[All,1]] (* Harvey P. Dale, Aug 08 2017 *)

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