A204769 - OEIS

%I #35 Feb 28 2023 02:23:42

%S 46,105,197,256,348,407,499,558,650,709,801,860,952,1011,1103,1162,

%T 1254,1313,1405,1464,1556,1615,1707,1766,1858,1917,2009,2068,2160,

%U 2219,2311,2370,2462,2521,2613,2672,2764,2823

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

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

%C Equivalently, numbers k such that k == 46 or 105 (mod 151). - _Bruno Berselli_, Mar 08 2012

%H Vincenzo Librandi, <a href="/A204769/b204769.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).

%F G.f.: x*(46+59*x+46*x^2)/((1+x)*(x-1)^2).

%F a(n) = (-151-33*(-1)^n+302*n)/4.

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

%F Sum_{n>=1} (-1)^(n+1)/a(n) = tan(59*Pi/302)*Pi/151. - _Amiram Eldar_, Feb 28 2023

%t 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}]

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

%o (PARI) a(n)=(-151-33*(-1)^n+302*n)/4 \\ _Charles R Greathouse IV_, Oct 16 2015

%Y 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.

%Y 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.

%K nonn,easy

%O 1,1

%A _Vincenzo Librandi_, Mar 08 2012