A056022 - OEIS

%I #23 Feb 19 2025 10:17:35

%S 1,18,19,30,31,48,50,67,68,79,80,97,99,116,117,128,129,146,148,165,

%T 166,177,178,195,197,214,215,226,227,244,246,263,264,275,276,293,295,

%U 312,313,324,325,342,344,361,362,373,374,391,393,410,411,422,423,440,442

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

%H Amiram Eldar, <a href="/A056022/b056022.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,0,0,0,1,-1).

%F From _Mike Sheppard_, Feb 18 2025 : (Start)

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

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

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

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

%t Select[ Range[ 500 ], PowerMod[ #, 6, 49 ]==1& ]

%t LinearRecurrence[{1, 0, 0, 0, 0, 1, -1}, {1, 18, 19, 30, 31, 48, 50}, 61] (* _Mike Sheppard_, Feb 18 2025 *)

%o (PARI) isok(k) = Mod(k, 49)^6 == 1; \\ _Michel Marcus_, Jun 30 2021

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

%K nonn,easy

%O 1,2

%A _Robert G. Wilson v_, Jun 08 2000