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A119344
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Integer lengths of Theodorus-primes: numbers n such that the concatenation of the first n decimal digits of the Theodorus's constant sqrt(3) is prime.
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4
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OFFSET
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1,1
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LINKS
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EXAMPLE
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sqrt(3) = 1.732050807568877..., so
a(1) = 2 (17 with 2 decimal digits is the 1st prime in the decimal expansion),
a(2) = 3 (173 with 3 decimal digits is the 2nd prime in the decimal expansion).
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MATHEMATICA
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nn = 1000; digs = RealDigits[Sqrt[3], 10, nn][[1]]; n = 0; t = {}; Do[n = 10*n + digs[[d]]; If[PrimeQ[n], AppendTo[t, d]], {d, nn}]; t (* T. D. Noe, Dec 05 2011 *)
Module[{nn=171000, c}, c=RealDigits[Sqrt[3], 10, nn][[1]]; Select[Range[ nn], PrimeQ[ FromDigits[Take[c, #]]]&]] (* Harvey P. Dale, May 13 2017 *)
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CROSSREFS
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Cf. A002194 (decimal expansion of sqrt(3)).
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KEYWORD
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nonn,more,base,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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