cp's OEIS Frontend

A071695 Lesser members of twin prime pairs of form (4*k+1, 4*k+3), k > 0.

%I A071695 #20 Jan 15 2019 20:21:41
%S A071695 5,17,29,41,101,137,149,197,269,281,461,521,569,617,641,809,821,857,
%T A071695 881,1049,1061,1229,1277,1289,1301,1481,1697,1721,1877,1949,1997,2081,
%U A071695 2129,2141,2237,2309,2381,2549,2657,2729,2789,2801,2969
%N A071695 Lesser members of twin prime pairs of form (4*k+1, 4*k+3), k > 0.
%C A071695 Corresponding greater members: A071696(n).
%C A071695 Or, lesser members of twin prime pairs (A001359) which are also Pythagorean primes (A002144). Intersection of A001359 and A002144. - _Zak Seidov_, Apr 25 2008
%C A071695 A010051(a(n)) * A010051(a(n)+2) = 1. - _Reinhard Zumkeller_, Nov 10 2013
%H A071695 Zak Seidov, <a href="/A071695/b071695.txt">Table of n, a(n) for n = 1..1000.</a>
%H A071695 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.
%t A071695 Select[ Prime@ Range@ 1000, Mod[#, 4] == 1 && PrimeQ[# + 2] &] (* _Robert G. Wilson v_, Jan 22 2012 *)
%o A071695 (PARI) p=2;forprime(q=3,1e4,if(q-p==2 && p%4==1, print1(p", "));p=q) \\ _Charles R Greathouse IV_, Mar 20 2013
%o A071695 (Haskell)
%o A071695 a071695 n = a071695_list !! (n-1)
%o A071695 a071695_list = [p | p <- a002144_list, a010051' (p + 2) == 1]
%o A071695 -- _Reinhard Zumkeller_, Nov 10 2013
%Y A071695 Cf. A001359, A002144, A071698, A071697.
%K A071695 nonn
%O A071695 1,1
%A A071695 _Reinhard Zumkeller_, Jun 04 2002