A119344 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.

2, 3, 19, 111, 116, 641, 5411, 170657

Offset: 1

Author

Eric W. Weisstein, May 15 2006

Keywords

• nonn
• more
• base
• hard

Examples

			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).
		

Links

• Eric Weisstein's World of Mathematics, Constant Primes
• Eric Weisstein's World of Mathematics, Integer Sequence Primes
• Eric Weisstein's World of Mathematics, Theodorus's Constant Digits

Crossrefs

Cf. A119343 (Theodorus-primes).

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

Programs

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 *)

Extensions

Edited by Charles R Greathouse IV, Apr 27 2010

a(8) = 170657 from Eric W. Weisstein, Aug 18 2013