A177046 a(n) = 127*(n-1)-a(n-1) with n>1, a(1)=16.

16, 111, 143, 238, 270, 365, 397, 492, 524, 619, 651, 746, 778, 873, 905, 1000, 1032, 1127, 1159, 1254, 1286, 1381, 1413, 1508, 1540, 1635, 1667, 1762, 1794, 1889, 1921, 2016, 2048, 2143, 2175, 2270, 2302, 2397, 2429, 2524, 2556, 2651, 2683, 2778, 2810, 2905, 2937, 3032, 3064

Offset: 1

Author

Vincenzo Librandi, Dec 09 2010

Keywords

• nonn
• easy

Comments

Positive numbers k such that k^2 == 2 (mod 127).

Links

• Index entries for linear recurrences with constant coefficients, signature (1,1,-1).

Programs

Magma

[(127-63*(-1)^(n-1)+254*(n-1))/(4): n in [1..50]];

Mathematica

LinearRecurrence[{1,1,-1},{16,111,143},50] (* Harvey P. Dale, May 30 2014 *)

Formula

a(n) = (127-63*(-1)^(n-1)+254*(n-1))/4.

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

G.f.: x*(16+95*x+16*x^2) / ( (1+x)*(x-1)^2 ). - R. J. Mathar, Aug 24 2011

Sum_{n>=1} (-1)^(n+1)/a(n) = cot(16*Pi/127)*Pi/127. - Amiram Eldar, Feb 28 2023