A232882 - OEIS

%I #19 Aug 26 2017 07:55:45

%S 17,19,71,73,107,109,179,181,197,199,269,271,431,433,521,523,809,811,

%T 827,829,881,883,1061,1063,1151,1153,1277,1279,1619,1621,1871,1873,

%U 1997,1999,2087,2089,2141,2143,2267,2269,2339,2341,2591,2593,2789,2791,2969

%N Twin primes with digital root 8 or 1.

%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 A232881 for {5,7}.

%C Twin primes of the form 9n +- 1. [_Bruno Berselli_, Aug 26 2014]

%e 17 and 19 are in the sequence because they form a twin prime pair in which 17 has a digital root of 8 and 19 has one of 1. Likewise 71 and 73 form a twin prime pair where 71 has 8 for a digital root and 73 has 1.

%t dRoot[n_] := 1 + Mod[n - 1, 9]; tw = Select[Prime[Range[1000]], PrimeQ[# + 2] &]; Select[Union[tw, tw + 2], MemberQ[{1, 8}, dRoot[#]] &] (* _T. D. Noe_, Dec 10 2013 *)

%Y Cf. A001097, A077800, A232880, A232881.

%K nonn,base

%O 1,1

%A _Gary Croft_, Dec 01 2013