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%I #26 May 13 2017 09:49:15
%S 2,3,19,111,116,641,5411,170657
%N 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.
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/ConstantPrimes.html">Constant Primes</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/IntegerSequencePrimes.html">Integer Sequence Primes</a>
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/TheodorussConstantDigits.html">Theodorus's Constant Digits</a>
%e sqrt(3) = 1.732050807568877..., so
%e a(1) = 2 (17 with 2 decimal digits is the 1st prime in the decimal expansion),
%e a(2) = 3 (173 with 3 decimal digits is the 2nd prime in the decimal expansion).
%t 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 *)
%t Module[{nn=171000,c},c=RealDigits[Sqrt[3],10,nn][[1]];Select[Range[ nn], PrimeQ[ FromDigits[Take[c,#]]]&]] (* _Harvey P. Dale_, May 13 2017 *)
%Y Cf. A119343 (Theodorus-primes).
%Y Cf. A002194 (decimal expansion of sqrt(3)).
%K nonn,more,base,hard
%O 1,1
%A _Eric W. Weisstein_, May 15 2006
%E Edited by _Charles R Greathouse IV_, Apr 27 2010
%E a(8) = 170657 from _Eric W. Weisstein_, Aug 18 2013
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