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

%I A177046 #31 Apr 13 2025 14:55:15
%S A177046 16,111,143,238,270,365,397,492,524,619,651,746,778,873,905,1000,1032,
%T A177046 1127,1159,1254,1286,1381,1413,1508,1540,1635,1667,1762,1794,1889,
%U A177046 1921,2016,2048,2143,2175,2270,2302,2397,2429,2524,2556,2651,2683,2778,2810,2905,2937,3032,3064
%N A177046 a(n) = 127*(n-1)-a(n-1) with n>1, a(1)=16.
%C A177046 Positive numbers k such that k^2 == 2 (mod 127).
%H A177046 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A177046 a(n) = (127-63*(-1)^(n-1)+254*(n-1))/4.
%F A177046 a(n) = a(n-1)+a(n-2)-a(n-3).
%F A177046 G.f.: x*(16+95*x+16*x^2) / ( (1+x)*(x-1)^2 ). - _R. J. Mathar_, Aug 24 2011
%F A177046 Sum_{n>=1} (-1)^(n+1)/a(n) = cot(16*Pi/127)*Pi/127. - _Amiram Eldar_, Feb 28 2023
%t A177046 LinearRecurrence[{1,1,-1},{16,111,143},50] (* _Harvey P. Dale_, May 30 2014 *)
%o A177046 (Magma) [(127-63*(-1)^(n-1)+254*(n-1))/(4): n in [1..50]];
%K A177046 nonn,easy
%O A177046 1,1
%A A177046 _Vincenzo Librandi_, Dec 09 2010