A020139 -id:A020139 - cp's OEIS frontend

A090084 Even pseudoprimes to base 11.

10, 70, 190, 1330, 8170, 9730, 24130, 28462, 58030, 98458, 143830, 144886, 327370, 856786, 1580230, 1620130, 3536470, 5274970, 6082490, 6376126, 6792710, 8066170, 8610610, 14076910, 17728930, 27275158, 42447406, 52970386, 53497978, 68925130

Offset: 1

Labos Elemer, Nov 25 2003

nonn

Amiram Eldar, Table of n, a(n) for n = 1..165 (terms below 10^11; terms 1..84 from Robert G. Wilson v)
Eric Weisstein's World of Mathematics, Fermat Pseudoprime.
Index entries for sequences related to pseudoprimes.

Cf. A020139.

Cf. A006935, A130433, A090082, A090083, A090085, A130434, A130435, A130436, A130438, A130439, A130440, A130441, A130442, A130443.

Do[ f=PowerMod[ 11, 2n-1, 2n ]; If[ f==1, Print[ 2n ] ],{n,2,800000} ] (* Alexander Adamchuk, May 26 2007 *)
lst = {}; Do[ If[ PowerMod[11, 2n - 1, 2n] == 1, AppendTo[lst, 2n]], {n, 2, 2*10^9}]; lst (* Robert G. Wilson v, Jun 01 2007 *)
Select[Range[4,68926000,2],PowerMod[11,#-1,#]==1&] (* Harvey P. Dale, Oct 16 2021 *)

is(k) = k > 2 && !(k % 2) &&  Mod(11, k)^(k-1) == 1; \\ Amiram Eldar, Sep 18 2024

More terms from Alexander Adamchuk, May 26 2007

Further terms from Robert G. Wilson v, Jun 01 2007

A020237 Strong pseudoprimes to base 11.

Original entry on oeis.org

133, 793, 2047, 4577, 5041, 12403, 13333, 14521, 17711, 23377, 43213, 43739, 47611, 48283, 49601, 50737, 50997, 56057, 58969, 68137, 74089, 85879, 86347, 87913, 88831, 102173, 111055, 114211, 115231, 137149, 139231, 171601, 172369, 193249, 196555

Offset: 1

David W. Wilson

nonn

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..636 from R. J. Mathar)
Index entries for sequences related to pseudoprimes

Cf. A020139, A001262, A020229, A020230, A020231, A020232, A020233, A020234, A020235, A020236.

/* insert A001262 code here */
isA020237(n)={
        isStrongPsp(n,11)
}
{
for(n=1,10000000000,
        if(isA020237(n), print(n) ;) ;
) ;
} /* R. J. Mathar, Mar 07 2012 */

A374976 Odd k with p^k mod k != p for all primes p.

Original entry on oeis.org

1, 9, 27, 63, 75, 81, 115, 119, 125, 189, 207, 209, 215, 235, 243, 279, 299, 319, 323, 387, 407, 413, 423, 515, 517, 531, 535, 551, 567, 575, 583, 611, 621, 623, 667, 675, 707, 713, 729, 731, 747, 767, 779, 783, 799, 815, 835, 851, 869, 893, 899, 917, 923, 927

Offset: 1

Francois R. Grieu, Jul 26 2024

nonn

Alternatively: 1, and odd composites not a pseudoprime to any prime base.

The sequence contains no primes, no pseudoprimes to any prime base (A001567, A005935, A005936, A005938, A020139, A020141...), and no Carmichael numbers (A002997).

			k=3 (resp. 5, 7) is not in the sequence because for prime p=2 it holds p^k mod k = 2 which is p.
k=9 is in the sequence because for prime p=2 (resp. 3, 5, 7) it holds p^k mod k = 8 (resp. 0, 8, 1) which is not p, and for all other primes p it holds p>=k therefore p^k mod k can't be p.

Francois R. Grieu, Table of n, a(n) for n = 1..10000

Cf. A000040, A001567, A005935, A005936, A005938, A020139, A020141, A020145, A002997.

Cases[Range[1, 930, 2], k_/; (For[p=2, p=k)]

cp's OEIS Frontend

A090084 Even pseudoprimes to base 11.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Extensions

A020237 Strong pseudoprimes to base 11.

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

A374976 Odd k with p^k mod k != p for all primes p.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica