A178958 Numbers n from A181780 that are not in A181781.

15, 28, 35, 39, 51, 52, 55, 63, 66, 70, 75, 76, 87, 95, 99, 111, 112, 115, 119, 123, 124, 130, 135, 143, 147, 148, 154, 155, 159, 171, 172, 176, 183, 186, 187, 190, 195, 196, 203, 207, 208, 215, 219, 232, 235, 238, 244, 246, 255, 267, 268, 275, 276, 279, 280, 286, 287, 291, 292, 295, 299

Offset: 1

Author

Karsten Meyer, Dec 31 2010

Keywords

• nonn

Comments

Numbers that are Fermat pseudoprimes to some base a (2<=a<=n-2) not Euler pseudoprimes to any base a (2<=a<=n-2).

Examples

			4^(15-1) == 1 (mod 15), but 4^((15-1)/2) == 4 (mod 15)
		

Crossrefs

A181780

Programs

PARI

fsp(n)=
{ /* whether n is Fermat pseudoprime to any base a where 2<=a<=n-2 */
    for (a=2,n-2,
        if ( gcd(a,n)!=1, next() );
        if ( (Mod(a,n))^(n-1)==+1, return(1) )
    );
    return(0);
}
esp(n)=
{ /* whether n is Euler pseudoprime to any base a where 2<=a<=n-2 */
    local(w);
    if ( n%2==0, return(0) );
    for (a=2,n-2,
        if ( gcd(a,n)!=1, next() );
        w = abs(component((Mod(a,n))^((n-1)/2),2));
        if ( (w==1) || (w==n-1), return(1) )
    );
    return(0);
}
for(n=3,300, if(isprime(n),next()); if( fsp(n) && (!esp(n)) , print1(n,", ") ); );