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

1,1

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).

Links

Table of n, a(n) for n=1..61.

Example

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

Prog

(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, ", ") ); );

Crossrefs

A181780

Sequence in context: A073766 A223449 A031334 * A099808 A291054 A134621

Adjacent sequences: A178955 A178956 A178957 * A178959 A178960 A178961

Keyword

nonn

Author

Karsten Meyer, Dec 31 2010

Status

approved