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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified November 20 12:30 EST 2017. Contains 294971 sequences.