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A238056 Primes which are the concatenation of two primes in exactly one way. 6
23, 37, 53, 73, 113, 137, 173, 193, 197, 211, 223, 229, 233, 241, 271, 283, 293, 311, 331, 337, 347, 353, 359, 367, 379, 383, 389, 397, 433, 523, 541, 547, 571, 593, 613, 617, 673, 677, 719, 733, 743, 761, 773, 977, 1013, 1033, 1093, 1097, 1117, 1123, 1129 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is not a duplicate of A129800, which accepts "07" for example as the second prime.

LINKS

Giovanni Resta, Table of n, a(n) for n = 1..5000

EXAMPLE

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.

MATHEMATICA

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 *)

PROG

(Haskell)

a238056 n = a238056_list !! (n-1)

a238056_list = filter ((== 1) . length . f) a000040_list where

  f x = filter (\(us, vs) ->

               head vs /= '0' &&

               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. A105184, A238057, A129800.

Cf. A010051, A000040.

Sequence in context: A272157 A129800 A105184 * A066064 A163759 A190731

Adjacent sequences:  A238053 A238054 A238055 * A238057 A238058 A238059

KEYWORD

nonn,base

AUTHOR

Colin Barker, Feb 17 2014

STATUS

approved

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Last modified August 5 01:51 EDT 2021. Contains 346456 sequences. (Running on oeis4.)