

A095303


Smallest number k such that k^n  2 is prime.


5



4, 2, 9, 3, 3, 3, 7, 7, 3, 21, 9, 7, 19, 5, 7, 39, 15, 61, 15, 19, 21, 3, 19, 17, 21, 5, 21, 7, 85, 17, 7, 21, 511, 27, 27, 59, 3, 19, 91, 45, 3, 29, 321, 65, 9, 379, 69, 125, 49, 5, 9, 45, 289, 341, 61, 89, 171, 171, 139, 21, 139, 75, 25, 49, 15, 51, 57, 175, 31, 137, 147, 25, 441
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OFFSET

1,1


COMMENTS

The Bunyakovsky conjecture implies a(n) exists for all n.  Robert Israel, Jul 15 2018
Some of the results were computed using the PrimeFormGW (PFGW) primalitytesting program.  Hugo Pfoertner, Nov 16 2019


LINKS

Robert Israel, Table of n, a(n) for n = 1..600
Wikipedia, Bunyakovsky conjecture


EXAMPLE

a(1) = 4 because 4^1  2 = 2 is prime, a(3) = 9 because 3^3  2 = 25, 5^3  2 = 123 and 7^3  2 = 341 = 11 * 31 are composite, whereas 9^3  2 = 727 is prime.


MAPLE

f:= proc(n) local k;
for k from 3 by 2 do
if isprime(k^n2) then return k fi
od
end proc:
f(1):= 4: f(2):= 2:
map(f, [$1..100]); # Robert Israel, Jul 15 2018


MATHEMATICA

a095303[n_] := For[k = 1, True, k++, If[PrimeQ[k^n  2], Return[k]]]; Array[a095303, 100] (* JeanFrançois Alcover, Mar 01 2019 *)


PROG

(PARI) for (n=1, 73, for(k=1, oo, if(isprime(k^n2), print1(k, ", "); break))) \\ Hugo Pfoertner, Oct 28 2018


CROSSREFS

Cf. A095304 (corresponding primes), A087576 (smallest k such that k^n+2 is prime), A095302 (corresponding primes).
Cf. A014224.
Sequence in context: A201574 A077809 A201281 * A060734 A075594 A076022
Adjacent sequences: A095300 A095301 A095302 * A095304 A095305 A095306


KEYWORD

nonn


AUTHOR

Hugo Pfoertner, Jun 01 2004


EXTENSIONS

a(2) and a(46) corrected by T. D. Noe, Apr 03 2012


STATUS

approved



