A020141 -id:A020141 - cp's OEIS frontend

A130435 Even pseudoprimes to base 13.

4, 6, 12, 244, 276, 2806, 5028, 10308, 40132, 51118, 115644, 185646, 216492, 237084, 789636, 936046, 941818, 1062876, 1237276, 1469716, 2119002, 2201002, 2410354, 2446426, 3198196, 4319052, 4979316, 5329468, 5496492, 7171876, 9513076

Offset: 1

Alexander Adamchuk, May 26 2007

nonn

Amiram Eldar, Table of n, a(n) for n = 1..300 (terms 1..101 from Robert G. Wilson v)
Eric Weisstein's World of Mathematics, Fermat Pseudoprime.
Index entries for sequences related to pseudoprimes.

Cf. A020141, A006935, A130433, A090082, A090083, A090084, A090085, A130434, A130436, A130437, A130438, A130439, A130440, A130441, A130442, A130443.

Do[ f=PowerMod[ 13, 2n-1, 2n ]; If[ f==1, Print[ 2n ] ], {n,2,1000000} ] (* Robert G. Wilson v, May 31 2007 *)

is(k) = k > 2 && !(k % 2) &&  Mod(13, k)^(k-1) == 1; \\ Amiram Eldar, Sep 18 2024

a(26)-a(31) from Robert G. Wilson v, May 31 2007

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

A130435 Even pseudoprimes to base 13.

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