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

Author

Colin Barker, Feb 17 2014

Keywords

• nonn
• base

Examples

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

Links

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

Crossrefs

Cf. A105184, A238056.

Cf. A010051, A000040.

Programs

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

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 *)