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A213740 a(n) is the smallest prime of the form n*m^q - 1 where m is an integer > 1 and q >= 2. 3
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 (list; graph; refs; listen; history; text; internal format)
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

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

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Last modified April 25 04:12 EDT 2019. Contains 322451 sequences. (Running on oeis4.)