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
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
KEYWORD
nonn,base,easy
AUTHOR
Gary Croft, Dec 01 2013
STATUS
approved