A238057 Primes which are the concatenation of two primes in exactly two ways.

313, 317, 373, 797, 1373, 1913, 1973, 1997, 2113, 2293, 2311, 2347, 2383, 2389, 2953, 2971, 3167, 3313, 3373, 3593, 3673, 3677, 3719, 3733, 3761, 4337, 4397, 5233, 5347, 5953, 6173, 6197, 6737, 7193, 7331, 7433, 7577, 7877, 7919, 7937, 10313, 10337, 10937

Offset

1,1

Links

Giovanni Resta, Table of n, a(n) for n = 1..1000

Example

313 is in the sequence because 31 and 3 are both primes, and 3 and 13 are both primes, so there are two ways.

Mathematica

spl[n_] := Block[{d = IntegerDigits@n, c = 0, z}, z = Length@d; Do[ If[ PrimeQ@ FromDigits@ Take[d, k] && d[[k + 1]] > 0 && PrimeQ@ FromDigits@ Take[d, k - z], c++], {k, z - 1}]; c]; Select[ Prime@ Range@1400, spl[#] == 2 &] (* Giovanni Resta, Feb 27 2014 *)

Prog

(Haskell)
a238057 n = a238057_list !! (n-1)
a238057_list = filter ((== 2) . length . f) a000040_list where
  f x = filter (\(us, vs) ->
               head vs /= '0' &&
               a010051' (read us :: Integer) == 1 &&
               a010051' (read vs :: Integer) == 1) $
               map (flip splitAt $ show x) [1 .. length (show x) - 1]
-- Reinhard Zumkeller, Feb 27 2014

Crossrefs

Cf. A105184, A238056.

Cf. A010051, A000040.

Sequence in context: A292197 A083972 A045275 * A097023 A159574 A139656

Adjacent sequences: A238054 A238055 A238056 * A238058 A238059 A238060

Keyword

nonn,base

Author

Colin Barker, Feb 17 2014

Status

approved