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

1,1

Links

Table of n, a(n) for n=1..8.

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

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. A119343 (Theodorus-primes).

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

Sequence in context: A009178 A141508 A366357 * A072877 A201378 A241350

Adjacent sequences: A119341 A119342 A119343 * A119345 A119346 A119347

Keyword

nonn,more,base,hard

Author

Eric W. Weisstein, May 15 2006

Extensions

Edited by Charles R Greathouse IV, Apr 27 2010

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

Status

approved