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 A232880 Twin primes with digital root 2 or 4. 8

%I

%S 11,13,29,31,101,103,137,139,191,193,227,229,281,283,461,463,569,571,

%T 641,643,659,661,821,823,857,859,1019,1021,1091,1093,1289,1291,1451,

%U 1453,1487,1489,1667,1669,1721,1723,2027,2029,2081,2083,2549,2551,2657,2659

%N Twin primes with digital root 2 or 4.

%C All twin primes except (3, 5) have one of 3 digital root pairings: {2, 4}, {5, 7} or {8, 1}: see A232881 for {5, 7} and A232882 for {8, 1}.

%C Or primes congruent to 11 or 13 mod 18 such that the number congruent to 13 or 11 mod 18 is also prime. - _Alonso del Arte_, Dec 02 2013

%e 11 and 13 are in the sequence because they form a twin prime pair in which 11 has a digital root of 2 and 13 has one of 4.

%e Likewise 29 and 31 form a twin prime pair with 29 has 2 for a digital root and 31 has 4.

%t partialList = Select[18Range[100] - 7, PrimeQ[#] && PrimeQ[# + 2] &]; A232880 = Sort[Flatten[Join[partialList, partialList + 2]]] (* _Alonso del Arte_, Dec 02 2013 *)

%t dRoot[n_] := 1 + Mod[n - 1, 9]; tw = Select[Prime[Range[1000]], PrimeQ[# + 2] &]; Select[Union[tw, tw + 2], MemberQ[{2, 4}, dRoot[#]] &] (* _T. D. Noe_, Dec 10 2013 *)

%o (PARI) p=5; forprime(q=7,1e4,if(q-p==2 && q%9==4, print1(p", "q", ")); p=q) \\ _Charles R Greathouse IV_, Aug 26 2014

%Y Cf. A001097, A077800, A232881, A232882.

%K nonn,base,easy

%O 1,1

%A _Gary Croft_, Dec 01 2013

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