A056027 Numbers k such that k^16 == 1 (mod 17^2).

1, 38, 40, 65, 75, 110, 131, 134, 155, 158, 179, 214, 224, 249, 251, 288, 290, 327, 329, 354, 364, 399, 420, 423, 444, 447, 468, 503, 513, 538, 540, 577, 579, 616, 618, 643, 653, 688, 709, 712, 733, 736, 757, 792, 802, 827, 829, 866, 868, 905, 907, 932, 942

Offset: 1

Author

Robert G. Wilson v, Jun 08 2000

Keywords

• nonn
• easy

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,-1).

Crossrefs

Cf. A056021, A056022, A056024, A056025, A056026, A056028, A056031, A056034, A056035.

Programs

Mathematica

x=17; Select[ Range[ 1000 ], PowerMod[ #, x-1, x^2 ]==1& ]
(* or *)
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 38, 40, 65, 75, 110, 131, 134, 155, 158, 179, 214, 224, 249, 251, 288, 290}, 55] (* Mike Sheppard, Feb 17 2025 *)

Formula

From Mike Sheppard, Feb 17 2025: (Start)

a(n) = a(n-1) + a(n-16) - a(n-17).

a(n) ~ (17^2/16) * n.

G.f.: (x*(1 + 37*x + 2*x^2 + 25*x^3 + 10*x^4 + 35*x^5 + 21*x^6 + 3*x^7 + 21*x^8 + 3*x^9 + 21*x^10 + 35*x^11 + 10*x^12 + 25*x^13 + 2*x^14 + 37*x^15 + x^16))/((1-x)*(1-x^16)).

(End)