A156718 Numbers k such that k^2 == -1 (mod 13^2).

70, 99, 239, 268, 408, 437, 577, 606, 746, 775, 915, 944, 1084, 1113, 1253, 1282, 1422, 1451, 1591, 1620, 1760, 1789, 1929, 1958, 2098, 2127, 2267, 2296, 2436, 2465, 2605, 2634, 2774, 2803, 2943, 2972, 3112, 3141, 3281, 3310, 3450, 3479, 3619, 3648, 3788

Offset: 1

Author

Vincenzo Librandi, Feb 14 2009

Keywords

• nonn
• easy

Comments

Also, numbers of the form 169k +- 70.

Links

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

Crossrefs

Cf. A156636, A156640, A156627, A156639.

Programs

Magma

[Floor(n/2)*169-70*(-1)^n: n in [1..50]];

Mathematica

LinearRecurrence[{1,1,-1},{70,99,239},50]

PARI

a(n)=n\2*169-70*(-1)^n \\ Charles R Greathouse IV, Dec 23 2011

Formula

a(n) = a(n-1) + a(n-2) - a(n-3).

G.f.: x*(70 + 29*x + 70*x^2) / ( (1+x)*(x-1)^2 ). - Alexander R. Povolotsky, Feb 15 2009

Sum_{n>=1} (-1)^(n+1)/a(n) = tan(29*Pi/338)*Pi/169. - Amiram Eldar, Feb 26 2023