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A191913
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Products of two distinct primes such that a concatenation of the factors (p||q or q||p) again is a product of two distinct primes.
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2
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15, 26, 34, 35, 38, 39, 55, 57, 69, 74, 85, 87, 91, 94, 95, 106, 115, 118, 119, 123, 134, 141, 145, 159, 161, 185, 187, 202, 205, 206, 209, 213, 215, 217, 221, 237, 254, 259, 265, 267, 287, 291, 295, 298, 301, 303, 309, 314, 319, 321, 334, 339, 346, 362, 365, 371, 377, 381, 382, 391, 393, 395, 398, 403, 407, 413, 415, 417, 437, 445
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OFFSET
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1,1
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COMMENTS
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Inspired by the calculation of sphenic chains, cf. link.
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LINKS
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EXAMPLE
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26=2*13 is in the sequence because 213 =3*71 is a product of two distinct primes.
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MATHEMATICA
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tdpQ[n_]:=Module[{fi=FactorInteger[n][[All, 1]]}, AnyTrue[ {fi[[1]]* 10^IntegerLength[fi[[2]]]+ fi[[2]], fi[[2]]*10^IntegerLength[ fi[[1]]]+ fi[[1]]}, PrimeNu[#]==PrimeOmega[#]==2&]]; Select[Range[ 500], PrimeOmega[#] == PrimeNu[#]==2&&tdpQ[#]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Jul 20 2018 *)
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PROG
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(PARI) for(i=1, 500, is_A006881(i)|next; f=factor(i); is_A006881(eval(Str(f[1, 1], f[2, 1]))) | is_A006881(eval(Str(f[2, 1], f[1, 1]))) & print1(i", "))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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