A056024 Numbers k such that k^10 == 1 (mod 11^2).

1, 3, 9, 27, 40, 81, 94, 112, 118, 120, 122, 124, 130, 148, 161, 202, 215, 233, 239, 241, 243, 245, 251, 269, 282, 323, 336, 354, 360, 362, 364, 366, 372, 390, 403, 444, 457, 475, 481, 483, 485, 487, 493, 511, 524, 565, 578, 596, 602, 604, 606, 608, 614, 632

Offset: 1

Author

Robert G. Wilson v, Jun 08 2000

Keywords

• nonn

Links

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

Crossrefs

Cf. A056021, A056022, A056025, A056026, A056027, A056028, A056031, A056034, A056035.

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

Programs

Mathematica

Select[ Range[ 800 ], PowerMod[ #, 10, 121 ]==1& ]
LinearRecurrence[{1, 0, 0, 0, 0, 0, 0, 0, 0, 1, -1}, {1, 3, 9, 27, 40, 81, 94, 112, 118, 120, 122}, 65] (* Mike Sheppard, Feb 19 2025 *)

Formula

From Mike Sheppard, Feb 19 2025: (Start)

a(n) = a(n-1) + a(n-10) - a(n-11).

a(n) = a(n-10) + 11^2.

a(n) ~ (11^2/10)*n. (End)