A056022 Numbers k such that k^6 == 1 (mod 7^2).

1, 18, 19, 30, 31, 48, 50, 67, 68, 79, 80, 97, 99, 116, 117, 128, 129, 146, 148, 165, 166, 177, 178, 195, 197, 214, 215, 226, 227, 244, 246, 263, 264, 275, 276, 293, 295, 312, 313, 324, 325, 342, 344, 361, 362, 373, 374, 391, 393, 410, 411, 422, 423, 440, 442

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 (1,0,0,0,0,1,-1).

Crossrefs

Cf. A056021, A056024, A056025, A056026, A056027, A056028, A056031, A056034, A056035.

Cf. A381319 (general case mod n^2).

Programs

Mathematica

Select[ Range[ 500 ], PowerMod[ #, 6, 49 ]==1& ]
LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {1, 18, 19, 30, 31, 48, 50}, 61] (* Mike Sheppard, Feb 18 2025 *)

PARI

isok(k) = Mod(k, 49)^6 == 1; \\ Michel Marcus, Jun 30 2021

Formula

From Mike Sheppard, Feb 18 2025 : (Start)

a(n) = a(n-1) + a(n-6) - a(n-7).

a(n) = a(n-6) + 7^2.

a(n) ~ (7^2/6)*n.

G.f.: (1 + x*(17 + x + 11*x^2 + x^3 + 17*x^4 + x^5))/(1 - x - x^6 + x^7). (End)