A232882 Twin primes with digital root 8 or 1.

17, 19, 71, 73, 107, 109, 179, 181, 197, 199, 269, 271, 431, 433, 521, 523, 809, 811, 827, 829, 881, 883, 1061, 1063, 1151, 1153, 1277, 1279, 1619, 1621, 1871, 1873, 1997, 1999, 2087, 2089, 2141, 2143, 2267, 2269, 2339, 2341, 2591, 2593, 2789, 2791, 2969

Offset: 1

Author

Gary Croft, Dec 01 2013

Keywords

• nonn
• base

Comments

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}.

Twin primes of the form 9n +- 1. [Bruno Berselli, Aug 26 2014]

Examples

			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.
		

Crossrefs

Cf. A001097, A077800, A232880, A232881.

Programs

Mathematica

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 *)