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

%I A129800 #10 Sep 16 2015 04:38:34
%S A129800 23,37,53,73,113,137,173,193,197,211,223,229,233,241,271,283,293,307,
%T A129800 311,331,337,347,353,359,367,379,383,389,397,433,503,523,541,547,571,
%U A129800 593,613,617,673,677,719,733,743,761,773,977,1013,1033,1093,1097,1103
%N A129800 Prime numbers that can be written as the concatenation of two other prime numbers in exactly one way.
%H A129800 Reinhard Zumkeller, <a href="/A129800/b129800.txt">Table of n, a(n) for n = 1..10000</a>
%e A129800 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.
%e A129800 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.
%t A129800 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 *)
%o A129800 (Haskell)
%o A129800 a129800 n = a129800_list !! (n-1)
%o A129800 a129800_list = filter ((== 1) . length . f) a000040_list where
%o A129800   f x = filter (\(us, vs) ->
%o A129800                a010051' (read us :: Integer) == 1 &&
%o A129800                a010051' (read vs :: Integer) == 1) $
%o A129800                map (flip splitAt $ show x) [1 .. length (show x) - 1]
%o A129800 -- _Reinhard Zumkeller_, Feb 27 2014
%Y A129800 Cf. A238056, A010051, A000040.
%K A129800 nonn,base
%O A129800 1,1
%A A129800 _Pierre CAMI_, Jun 03 2007
%E A129800 More terms from _Stefan Steinerberger_, Jun 04 2007