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A232881 Twin primes with digital root 5 or 7. 6

%I

%S 5,41,59,149,239,311,347,419,599,617,1031,1049,1229,1301,1319,1427,

%T 1481,1607,1697,1787,1877,1931,1949,2111,2129,2237,2309,2381,2687,

%U 3119,3299,3371,3389,3461,3767,3821,3929,4001,4019,4091,4127,4217,4271,4649,4721

%N Twin primes with digital root 5 or 7.

%C All twin primes except (3,5) have one of 3 digital root pairings: {2,4}, {5,7} or {8,1}: see A232880 for {2,4} and A232882 for {8,1}.

%e 41 and 43 are in the sequence because they form a twin prime pair in which 41 has a digital root of 5 and 43 has a digital root of 7. Likewise 59 and 61 form a twin prime pair where 59 has a digital root of 5 and 61 has one of 7.

%t dRoot[n_] := 1 + Mod[n - 1, 9]; tw = Select[Prime[Range[1000]], PrimeQ[# + 2] &]; Select[Union[tw, tw + 2], MemberQ[{5, 7}, dRoot[#]] &] (* _T. D. Noe_, Dec 10 2013 *)

%Y Cf. A001097, A077800, A232880, A232882.

%K nonn,base

%O 1,1

%A _Gary Croft_, Dec 01 2013

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Last modified June 25 11:31 EDT 2017. Contains 288709 sequences.