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A232881 Twin primes with digital root 5 or 7. 6
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 (list; graph; refs; listen; history; text; internal format)
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 A232880 for {2,4} and A232882 for {8,1}.

LINKS

Table of n, a(n) for n=1..45.

EXAMPLE

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.

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 *)

CROSSREFS

Cf. A001097, A077800, A232880, A232882.

Sequence in context: A010573 A043083 A041599 * A174054 A106963 A276916

Adjacent sequences:  A232878 A232879 A232880 * A232882 A232883 A232884

KEYWORD

nonn,base

AUTHOR

Gary Croft, Dec 01 2013

STATUS

approved

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Last modified April 29 19:06 EDT 2017. Contains 285613 sequences.