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A071698 Lesser members of twin prime pairs of form (4*k+3, 4*k+5), k >= 0. 10

%I #26 Sep 08 2022 08:45:06

%S 3,11,59,71,107,179,191,227,239,311,347,419,431,599,659,827,1019,1031,

%T 1091,1151,1319,1427,1451,1487,1607,1619,1667,1787,1871,1931,2027,

%U 2087,2111,2267,2339,2591,2687,2711,2999,3119,3167,3251,3299

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

%C Corresponding greater members: A071699(n).

%H Reinhard Zumkeller, <a href="/A071698/b071698.txt">Table of n, a(n) for n = 1..10000</a>

%H Alexei Kourbatov and Marek Wolf, <a href="http://arxiv.org/abs/1901.03785">Predicting maximal gaps in sets of primes</a>, arXiv preprint arXiv:1901.03785 [math.NT], 2019.

%F a(n) = 2*A241557(n+1)-1. - _Hilko Koning_, Nov 06 2019

%t 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 *)

%o (Haskell)

%o a071698 n = a071698_list !! (n-1)

%o a071698_list = [x | x <- [3, 7 ..], a010051' x == 1, a010051' (x+2) == 1]

%o -- _Reinhard Zumkeller_, Aug 05 2014

%o (Magma) [4*k+3:k in [0..1000]|IsPrime(4*k+3) and IsPrime(4*k+5)]; // _Marius A. Burtea_, Nov 06 2019

%Y Cf. A001359, A071695, A071700.

%Y Cf. A010051, subsequence of A004767.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jun 04 2002

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Last modified March 28 14:38 EDT 2024. Contains 371254 sequences. (Running on oeis4.)