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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. 4
2, 3, 19, 111, 116, 641, 5411, 170657 (list; graph; refs; listen; history; text; internal format)
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: A072263 A009178 A141508 * 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

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Last modified July 22 20:49 EDT 2019. Contains 325226 sequences. (Running on oeis4.)