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

1,1

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.

Links

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

Formula

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000045, A054643, A122535, A006562.

Sequence in context: A366213 A061424 A140371 * A142511 A236070 A059705

Adjacent sequences: A181421 A181422 A181423 * A181425 A181426 A181427

Keyword

nonn

Author

Carmine Suriano, Oct 18 2010

Status

approved