A156702 Numbers k such that k^2 - 1 == 0 (mod 24^2).

1, 127, 161, 287, 289, 415, 449, 575, 577, 703, 737, 863, 865, 991, 1025, 1151, 1153, 1279, 1313, 1439, 1441, 1567, 1601, 1727, 1729, 1855, 1889, 2015, 2017, 2143, 2177, 2303, 2305, 2431, 2465, 2591, 2593, 2719, 2753, 2879, 2881, 3007, 3041, 3167, 3169

Offset: 1

Author

Vincenzo Librandi, Feb 13 2009

Keywords

• nonn
• easy

Comments

Numbers k that are == +-1 (mod 9) and == +-1 (mod 32). - Charles R Greathouse IV, Dec 23 2011

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..1000
• Index entries for linear recurrences with constant coefficients, signature (1,0,0,1,-1).

Programs

Mathematica

LinearRecurrence[{1,0,0,1,-1},{1,127,161,287,289},50] (* Vincenzo Librandi, Feb 08 2012 *)
With[{c=24^2},Select[Range[3200],Divisible[#^2-1,c]&]] (* Harvey P. Dale, Apr 25 2012 *)

PARI

a(n)=n\4*288+[-1,1,127,161][n%4+1]

Formula

G.f.: (-x^4 + 2*x^3 + 126*x^2 + 34*x + 127)/(x^5 - x^4 - x + 1). - Alexander R. Povolotsky, Feb 15 2009

a(n) = -36 + 27*(-1)^n + (4-4*i)*(-i)^n + (4+4*i)*i^n + 72*n. - Harvey P. Dale, Apr 25 2012

Sum_{n>=1} (-1)^(n+1)/a(n) = (cot(Pi/288) - tan(17*Pi/288))*Pi/288. - Amiram Eldar, Feb 26 2023

E.g.f.: 1 + 8*cos(x) + 9*(8*x - 1)*cosh(x) - 8*sin(x) + 9*(8*x - 7)*sinh(x). - Stefano Spezia, Oct 13 2024

Extensions

Corrected and edited by Vinay Vaishampayan, Jun 23 2010