

A129802


Possible bases for Pepin's primality test for Fermat numbers.


0



3, 5, 6, 7, 10, 12, 14, 20, 24, 27, 28, 39, 40, 41, 45, 48, 51, 54, 56, 63, 65, 75, 78, 80, 82, 85, 90, 91, 96, 102, 105, 108, 112, 119, 125, 126, 130, 147, 150, 156, 160, 164, 170, 175, 180, 182, 192, 204, 210, 216, 224, 238, 243, 245, 250, 252, 260, 291, 294, 300
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OFFSET

1,1


COMMENTS

Prime elements of this sequence are given by A102742.


LINKS

Table of n, a(n) for n=1..60.
Eric Weisstein's World of Mathematics, Pepin's Test


FORMULA

A positive integer 2^k*m, where m is odd and k>=0, belongs to this sequence iff the Jacobi symbol (F_n/m)=1 only for a finite number of Fermat numbers F_n=A000215(n).


PROG

(PARI) { isPepin(n) = local(s, S=Set(), t); n\=2^valuation(n, 2); s=Mod(3, n); while( !setsearch(S, s), S=setunion(S, [s]); s=(s1)^2+1); t=s; until( t==s, if( kronecker(lift(t), n)==1, return(0)); t=(t1)^2+1); 1 } for(n=2, 1000, if(isPepin(n), print1(n, ", ")))


CROSSREFS

Cf. A000215, A019434, A060377, A102742.
Sequence in context: A028811 A034035 A136804 * A023854 A092559 A064728
Adjacent sequences: A129799 A129800 A129801 * A129803 A129804 A129805


KEYWORD

nonn


AUTHOR

Max Alekseyev, Jun 14 2007, corrected Dec 29 2007. Thanks to Ant King for pointing out an error in the earlier version of this sequence.


STATUS

approved



