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A178958 Numbers n from A181780 that are not in A181781. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 16 21:23 EST 2020. Contains 331975 sequences. (Running on oeis4.)