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Greater members of twin prime pairs of form (4*k+1,4*k+3), k>0.
10

%I #10 Sep 10 2024 16:36:28

%S 7,19,31,43,103,139,151,199,271,283,463,523,571,619,643,811,823,859,

%T 883,1051,1063,1231,1279,1291,1303,1483,1699,1723,1879,1951,1999,2083,

%U 2131,2143,2239,2311,2383,2551,2659,2731,2791,2803,2971

%N Greater members of twin prime pairs of form (4*k+1,4*k+3), k>0.

%C Corresponding lesser members: A071695(n).

%C A010051(a(n)) * A010051(a(n)-2) = 1. - _Reinhard Zumkeller_, Nov 10 2013

%H Reinhard Zumkeller, <a href="/A071696/b071696.txt">Table of n, a(n) for n = 1..10000</a>

%t Select[Partition[Prime[Range[500]],2,1],#[[2]]-#[[1]]==2&&IntegerQ[ (#[[1]]-1)/4]&][[All,2]] (* _Harvey P. Dale_, Aug 27 2021 *)

%t Select[Table[4k+{1,3},{k,750}],AllTrue[#,PrimeQ]&][[;;,2]] (* _Harvey P. Dale_, Sep 10 2024 *)

%o (Haskell)

%o a071696 n = a071696_list !! (n-1)

%o a071696_list = [p | p <- tail a002145_list, a010051' (p - 2) == 1]

%o -- _Reinhard Zumkeller_, Nov 10 2013

%Y Cf. A006512, A071699, A071697.

%Y Cf. Subsequence of A002145.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jun 04 2002