A213740 a(n) is the smallest prime of the form n*m^q - 1 where m is an integer > 1 and q >= 2.

3, 7, 11, 31, 19, 23, 223, 31, 71, 79, 43, 47, 103, 223, 59, 127, 67, 71, 151, 79, 83, 197, 367, 191, 199, 103, 107, 223, 463, 239, 991, 127, 131, 271, 139, 971, 11987, 151, 311, 359, 163, 167, 5503, 1187, 179, 367, 751, 191, 1567, 199, 5099, 467, 211, 431

Offset

1,1

Links

Michel Marcus, Table of n, a(n) for n = 1..10000

Example

a(10) = 79 = 10*2^3 - 1.

Maple

f:= proc(n) local m, k, p, x, xm, dm;
p:= 1; xm:= infinity;
if n::odd then dm:= 2 else dm:= 1 fi;
do
   p:= nextprime(p);
   if n*2^p-1 > xm then return xm fi;
   if not irreduc(n*X^p-1) then next fi;
   for m from 2 by dm do
     x:= n*m^p-1;
     if x > xm then break fi;
     if isprime(x) then xm:= x; break fi;
   od
od
end proc:
f(1):= 3:
map(f, [$1..100]); # Robert Israel, Feb 26 2018

Mathematica

a[n_] := Module[{p, qq}, For[p = 2, True, p = NextPrime[p], qq = (p+1)/n; If[Denominator[qq] == 1 && GCD @@ FactorInteger[qq][[All, 2]] > 1, Return[p]]]];
Table[a[n], {n, 1, 100}] (* Jean-François Alcover, Feb 08 2023, after Michel Marcus *)

Prog

(PARI) a(n) = {forprime(p=2, , qq = (p+1)/n; if ((denominator(qq) == 1) && ispower(qq), return (p)); ); } \\ Michel Marcus, Feb 25 2018

Crossrefs

Cf. A001597, A213738.

Sequence in context: A125879 A238673 A318263 * A267357 A152084 A274134

Adjacent sequences: A213737 A213738 A213739 * A213741 A213742 A213743

Keyword

nonn

Author

Michel Lagneau, Jun 19 2012

Status

approved