A056025 Numbers k such that k^12 == 1 (mod 13^2).

1, 19, 22, 23, 70, 80, 89, 99, 146, 147, 150, 168, 170, 188, 191, 192, 239, 249, 258, 268, 315, 316, 319, 337, 339, 357, 360, 361, 408, 418, 427, 437, 484, 485, 488, 506, 508, 526, 529, 530, 577, 587, 596, 606, 653, 654, 657, 675, 677, 695, 698, 699, 746

Offset

1,2

Comments

From 19 to 168 inclusive, these are the numbers that 'fool' the strong pseudoprimality test described in Wilf (1986) in regard to determining whether 169 is composite. - Alonso del Arte, Feb 05 2012

References

Herbert S. Wilf, Algorithms and Complexity, Englewood Cliffs, New Jersey: Prentice-Hall, 1986, pp. 158-160.

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000

Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,1,-1).

Formula

From Mike Sheppard, Feb 19 2025 : (Start)

a(n) = a(n-1) + a(n-12) - a(n-13).

a(n) = a(n-12) + 13^2.

a(n) ~ (13^2/12)*n. (End)

Mathematica

Select[ Range[ 800 ], PowerMod[ #, 12, 169 ]==1& ]
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 19, 22, 23, 70, 80, 89, 99, 146, 147, 150, 168, 170}, 56] (* Mike Sheppard, Feb 19 2025 *)

Prog

(PARI) is(k)=Mod(k, 169)^12==1 \\ Charles R Greathouse IV, Feb 07 2018

Crossrefs

Cf. A056021, A056022, A056024, A056026, A056027, A056028, A056031, A056034, A056035.

Sequence in context: A167998 A050714 A113868 * A284670 A099954 A335347

Adjacent sequences: A056022 A056023 A056024 * A056026 A056027 A056028

Keyword

nonn,easy

Author

Robert G. Wilson v, Jun 08 2000

Extensions

Definition corrected by T. D. Noe, Aug 23 2008

Status

approved