

A232880


Twin primes with digital root 2 or 4.


8



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
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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(qp==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



