A071698 Lesser members of twin prime pairs of form (4*k+3, 4*k+5), k >= 0.

3, 11, 59, 71, 107, 179, 191, 227, 239, 311, 347, 419, 431, 599, 659, 827, 1019, 1031, 1091, 1151, 1319, 1427, 1451, 1487, 1607, 1619, 1667, 1787, 1871, 1931, 2027, 2087, 2111, 2267, 2339, 2591, 2687, 2711, 2999, 3119, 3167, 3251, 3299

Offset: 1

Author

Reinhard Zumkeller, Jun 04 2002

Keywords

• nonn

Comments

Corresponding greater members: A071699(n).

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
• Alexei Kourbatov and Marek Wolf, Predicting maximal gaps in sets of primes, arXiv preprint arXiv:1901.03785 [math.NT], 2019.

Crossrefs

Cf. A001359, A071695, A071700.

Cf. A010051, subsequence of A004767.

Programs

Haskell

a071698 n = a071698_list !! (n-1)
a071698_list = [x | x <- [3, 7 ..], a010051' x == 1, a010051' (x+2) == 1]
-- Reinhard Zumkeller, Aug 05 2014

Magma

[4*k+3:k in [0..1000]|IsPrime(4*k+3) and IsPrime(4*k+5)]; // Marius A. Burtea, Nov 06 2019

Mathematica

Transpose[Select[Table[4n+{3,5},{n,0,1000}],AllTrue[#,PrimeQ]&]][[1]] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Jan 16 2015 *)

Formula

a(n) = 2*A241557(n+1)-1. - Hilko Koning, Nov 06 2019