A232880 Twin primes with digital root 2 or 4.

11, 13, 29, 31, 101, 103, 137, 139, 191, 193, 227, 229, 281, 283, 461, 463, 569, 571, 641, 643, 659, 661, 821, 823, 857, 859, 1019, 1021, 1091, 1093, 1289, 1291, 1451, 1453, 1487, 1489, 1667, 1669, 1721, 1723, 2027, 2029, 2081, 2083, 2549, 2551, 2657, 2659

Offset

1,1

Comments

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}.

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

Links

Table of n, a(n) for n=1..48.

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A001097, A077800, A232881, A232882.

Sequence in context: A067786 A132245 A140567 * A117314 A115560 A045466

Adjacent sequences: A232877 A232878 A232879 * A232881 A232882 A232883

Keyword

nonn,base,easy

Author

Gary Croft, Dec 01 2013

Status

approved