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
KEYWORD
base,nonn
AUTHOR
Amarnath Murthy, Jun 02 2004
EXTENSIONS
Corrected and extended by Wouter Meeussen, Jun 04 2004
STATUS
approved