

A129800


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


4



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
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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 !! (n1)
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



