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

1,1

Links

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

Example

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.

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 *)

Prog

(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

Crossrefs

Cf. A238056, A010051, A000040.

Sequence in context: A057878 A019549 A272157 * A105184 A238056 A066064

Adjacent sequences: A129797 A129798 A129799 * A129801 A129802 A129803

Keyword

nonn,base

Author

Pierre CAMI, Jun 03 2007

Extensions

More terms from Stefan Steinerberger, Jun 04 2007

Status

approved