A095189 Smallest prime formed by the digit string after decimal point of n^(1/n), or 0 if no such prime exists.

0, 41, 442249570307408382321638310780109588391, 41, 3, 3, 3, 2, 2, 2, 2, 2, 2, 2, 19, 189207115002721, 181, 17, 167, 16158634964154228180872122424567684345543663819, 15601, 15085130035827878542455979623747888891433345604817588712723282399687865427853871, 1460552582234841803

Offset

1,2

Comments

Conjecture: a(n) is nonzero for all n>1. Generates surprisingly large primes that are easily certified using Elliptic curve techniques (Mathematica's NumberTheory`PrimeQ`). For n=24 no certifiable prime was found with fewer than 1024 digits. - Wouter Meeussen, Jun 04 2004

a(24) is a 3932-digit number; see the a-file from Robert G. Wilson v in the Links section. - Jon E. Schoenfield, Jul 31 2021

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..23

Robert G. Wilson v, Table of n, a(n) with a(n) = 'Unknown' where not known

Example

a(7) = 3 as 7^(1/7) = 1.3204692477561... and the least prime is 3.

Mathematica

<< NumberTheory`PrimeQ`; Table[{n, k = 1; While[temp = Floor[10^k FractionalPart[n^(1/n)]]; k < 256 && (temp === 1 || ! ProvablePrimeQ[temp]), k++ ]; temp, k}, {n, 2, 23}]
f[n_] := f[n] = Block[{k = 1, c = FractionalPart[n^(1/n)]}, While[d = FromDigits[ RealDigits[c, 10, k][[1]]]; k < 10001 && ! PrimeQ[d], k++; j = k]; If[k == 10001, 0, d]]; f[1] = 0; Array[f, 23] (* Robert G. Wilson v, Oct 11 2014 *)

Crossrefs

Cf. A095188.

Sequence in context: A297058 A125194 A237639 * A023932 A243831 A022074

Adjacent sequences: A095186 A095187 A095188 * A095190 A095191 A095192

Keyword

base,nonn

Author

Amarnath Murthy, Jun 02 2004

Extensions

Corrected and extended by Wouter Meeussen, Jun 04 2004

Status

approved