A204766 -id:A204766 - cp's OEIS frontend

A204769 a(n) = 151*(n-1) - a(n-1) with n>1, a(1)=46.

46, 105, 197, 256, 348, 407, 499, 558, 650, 709, 801, 860, 952, 1011, 1103, 1162, 1254, 1313, 1405, 1464, 1556, 1615, 1707, 1766, 1858, 1917, 2009, 2068, 2160, 2219, 2311, 2370, 2462, 2521, 2613, 2672, 2764, 2823

Offset: 1

Vincenzo Librandi, Mar 08 2012

Positive numbers k such that k^2 == 2 (mod 151), where the prime 151 == -1 (mod 8).

Equivalently, numbers k such that k == 46 or 105 (mod 151). - Bruno Berselli, Mar 08 2012

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

Sequences of the type n^2 == 2 (mod p), where p is a prime of the form 8k-1: A047341, A155450, A164131, A164135, A167533, A167534, A177044, A177046, A204766.

Sequences of the type n^2 == 2 (mod p), where p is a prime of the form 8k+1: A155449, A158803, A159007, A159008, A176010, A206525.

[(-151-33*(-1)^n+302*n)/4: n in [1..60]];

LinearRecurrence[{1,1,-1}, {46,105,197}, 40] (* or *) CoefficientList[Series[x*(46+59*x+46*x^2)/((1+x)*(x-1)^2),{x,0,33}],x] (* or *) a[1] = 46; a[n_] := a[n] = 151*(n-1) - a[n-1]; Table[a[n], {n, 1, 40}]

a(n)=(-151-33*(-1)^n+302*n)/4 \\ Charles R Greathouse IV, Oct 16 2015

G.f.: x*(46+59*x+46*x^2)/((1+x)*(x-1)^2).
a(n) = (-151-33*(-1)^n+302*n)/4.
a(n) = a(n-1) +a(n-2) -a(n-3).
Sum_{n>=1} (-1)^(n+1)/a(n) = tan(59*Pi/302)*Pi/151. - Amiram Eldar, Feb 28 2023

cp's OEIS Frontend

A204769 a(n) = 151*(n-1) - a(n-1) with n>1, a(1)=46.

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