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

1,1

Comments

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

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A105184, A238057, A129800.

Cf. A010051, A000040.

Sequence in context: A272157 A129800 A105184 * A066064 A163759 A190731

Adjacent sequences: A238053 A238054 A238055 * A238057 A238058 A238059

Keyword

nonn,base

Author

Colin Barker, Feb 17 2014

Status

approved