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

%I A238056 #16 Feb 27 2014 10:56:00
%S A238056 23,37,53,73,113,137,173,193,197,211,223,229,233,241,271,283,293,311,
%T A238056 331,337,347,353,359,367,379,383,389,397,433,523,541,547,571,593,613,
%U A238056 617,673,677,719,733,743,761,773,977,1013,1033,1093,1097,1117,1123,1129
%N A238056 Primes which are the concatenation of two primes in exactly one way.
%C A238056 This is not a duplicate of A129800, which accepts "07" for example as the second prime.
%H A238056 Giovanni Resta, <a href="/A238056/b238056.txt">Table of n, a(n) for n = 1..5000</a>
%e A238056 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.
%t A238056 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 *)
%o A238056 (Haskell)
%o A238056 a238056 n = a238056_list !! (n-1)
%o A238056 a238056_list = filter ((== 1) . length . f) a000040_list where
%o A238056   f x = filter (\(us, vs) ->
%o A238056                head vs /= '0' &&
%o A238056                a010051' (read us :: Integer) == 1 &&
%o A238056                a010051' (read vs :: Integer) == 1) $
%o A238056                map (flip splitAt $ show x) [1 .. length (show x) - 1]
%o A238056 -- _Reinhard Zumkeller_, Feb 27 2014
%Y A238056 Cf. A105184, A238057, A129800.
%Y A238056 Cf. A010051, A000040.
%K A238056 nonn,base
%O A238056 1,1
%A A238056 _Colin Barker_, Feb 17 2014