A181424 Primes p such that p and the two previous primes are in arithmetic progression.

7, 59, 163, 179, 223, 263, 269, 379, 569, 599, 613, 659, 739, 953, 983, 1109, 1129, 1193, 1229, 1373, 1523, 1753, 1759, 1913, 2293, 2423, 2683, 2909, 2969, 3313, 3319, 3643, 3739, 4019, 4421, 4463, 4603, 4663, 4703, 4999, 5113, 5119, 5309, 5393, 5399

Offset: 1

Author

Carmine Suriano, Oct 18 2010

Keywords

• nonn

Comments

Call d(i)=p(i+2)-p(i+1) and dd(i)=d(i+1)-d(i) then dd(i)=0.

All related first differences are multiples of 6 except the first one, which is 2.

Examples

			a(7)=269 since d(269,263)=6 and d(263,257)=6 and their difference is 0.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000045, A054643, A122535, A006562.

Programs

Haskell

a181424 = a000040 . (+ 2) . a064113  -- Reinhard Zumkeller, Jan 20 2012

Mathematica

Select[Partition[Prime[Range[750]],3,1],Length[Union[Differences[#]]]==1&][[;;,3]] (* Harvey P. Dale, Oct 09 2023 *)

Formula

a(n) = A000040(A064113(n) + 2). - Reinhard Zumkeller, Jan 20 2012