A232881 Twin primes with digital root 5 or 7.

5, 41, 59, 149, 239, 311, 347, 419, 599, 617, 1031, 1049, 1229, 1301, 1319, 1427, 1481, 1607, 1697, 1787, 1877, 1931, 1949, 2111, 2129, 2237, 2309, 2381, 2687, 3119, 3299, 3371, 3389, 3461, 3767, 3821, 3929, 4001, 4019, 4091, 4127, 4217, 4271, 4649, 4721

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 A232882 for {8,1}.

Examples

			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.
		

Crossrefs

Cf. A001097, A077800, A232880, A232882.

Programs

Mathematica

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 *)