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 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Prime elements of this sequence are given by A102742. LINKS 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=(s-1)^2+1); t=s; until( t==s, if( kronecker(lift(t), n)==1, return(0)); t=(t-1)^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 A242076 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

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