

A119344


Integer lengths of Theodorusprimes: numbers n such that the concatenation of the first n decimal digits of the Theodorus's constant sqrt(3) is prime.


4




OFFSET

1,1


LINKS



EXAMPLE

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).


MATHEMATICA

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 *)


CROSSREFS

Cf. A002194 (decimal expansion of sqrt(3)).


KEYWORD

nonn,more,base,hard


AUTHOR



EXTENSIONS



STATUS

approved



