A238056 Primes which are the concatenation of two primes in exactly one way.

23, 37, 53, 73, 113, 137, 173, 193, 197, 211, 223, 229, 233, 241, 271, 283, 293, 311, 331, 337, 347, 353, 359, 367, 379, 383, 389, 397, 433, 523, 541, 547, 571, 593, 613, 617, 673, 677, 719, 733, 743, 761, 773, 977, 1013, 1033, 1093, 1097, 1117, 1123, 1129

Offset: 1

Author

Colin Barker, Feb 17 2014

Keywords

• nonn
• base

Comments

This is not a duplicate of A129800, which accepts "07" for example as the second prime.

Examples

			113 is in the sequence because 11 and 3 are both primes, but 1 and 13 are not both primes, so there is one way.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..5000

Crossrefs

Cf. A105184, A238057, A129800.

Cf. A010051, A000040.

Programs

Haskell

a238056 n = a238056_list !! (n-1)
a238056_list = filter ((== 1) . 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@ 300, spl[#] == 1 &] (* Giovanni Resta, Feb 27 2014 *)