A129800 Prime numbers that can be written as the concatenation of two other prime numbers in exactly one way.

23, 37, 53, 73, 113, 137, 173, 193, 197, 211, 223, 229, 233, 241, 271, 283, 293, 307, 311, 331, 337, 347, 353, 359, 367, 379, 383, 389, 397, 433, 503, 523, 541, 547, 571, 593, 613, 617, 673, 677, 719, 733, 743, 761, 773, 977, 1013, 1033, 1093, 1097, 1103

Offset: 1

Author

Pierre CAMI, Jun 03 2007

Keywords

• nonn
• base

Examples

			113 is a prime number and the concatenation of two prime numbers: (11)(3). This decomposition is unique because (1)(13) is not valid since 1 is not a prime.
However 313 can be seen as both (31)(3) and (3)(13), hence there is no unique decomposition and 313 is not in the sequence.
		

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A238056, A010051, A000040.

Programs

Haskell

a129800 n = a129800_list !! (n-1)
a129800_list = filter ((== 1) . length . f) a000040_list where
  f x = filter (\(us, vs) ->
               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

a = {}; For[n = 5, n < 200, n++, b = IntegerDigits[Prime[n]]; in = 0; For[j = 1, j < Length[b], j++, If[PrimeQ[FromDigits[Take[b, j]]] && PrimeQ[FromDigits[Drop[ b, j]]], in++ ]]; If[in == 1, AppendTo[a, Prime[n]]]]; a (* Stefan Steinerberger, Jun 04 2007 *)

Extensions

More terms from Stefan Steinerberger, Jun 04 2007