%I #30 Sep 08 2022 08:44:57

%S 1,2,7,9,10,15,17,18,23,25,26,31,33,34,39,41,42,47,49,50,55,57,58,63,

%T 65,66,71,73,74,79,81,82,87,89,90,95,97,98,103,105,106,111,113,114,

%U 119,121,122,127,129,130,135,137,138,143,145,146,151,153,154,159

%N Numbers that are congruent to {1, 2, 7} mod 8.

%C Numbers h such that Fibonacci(h) mod 3 = 1. - _Bruno Berselli_, Oct 18 2017

%H G. C. Greubel, <a href="/A047526/b047526.txt">Table of n, a(n) for n = 1..1000</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).

%F From _Chai Wah Wu_, May 30 2016: (Start)

%F a(n) = a(n-1) + a(n-3) - a(n-4), for n > 4.

%F G.f.: x*(x^3 + 5*x^2 + x + 1)/(x^4 - x^3 - x + 1). (End)

%F From _Wesley Ivan Hurt_, Jun 10 2016: (Start)

%F a(n) = 8*n/3 - 2 + cos(2*n*Pi/3) + 5*sin(2*n*Pi/3)/(3*sqrt(3)).

%F a(3*k) = 8*k-1, a(3*k-1) = 8*k-6, a(3*k-2) = 8*k-7. (End)

%F Sum_{n>=1} (-1)^(n+1)/a(n) = ((2*sqrt(2+sqrt(2))-1)*Pi + log(3 - 2*sqrt(2)))/(8*sqrt(2)). - _Amiram Eldar_, Dec 19 2021

%p A047526:=n->8*n/3-2+cos(2*n*Pi/3)+5*sin(2*n*Pi/3)/(3*sqrt(3)): seq(A047526(n), n=1..100); # _Wesley Ivan Hurt_, Jun 10 2016

%t LinearRecurrence[{1, 0, 1, -1}, {1, 2, 7, 9}, 50] (* _G. C. Greubel_, May 30 2016 *)

%t #+{1,2,7}&/@(8*Range[0,20])//Flatten (* _Harvey P. Dale_, Oct 17 2021 *)

%o (Magma) [n: n in [0..150] | n mod 8 in [1,2,7]]; // _Wesley Ivan Hurt_, Jun 10 2016

%Y Cf. A000045.

%Y Cf. A008586 (numbers h such that Fibonacci(h) mod 3 = 0).

%Y Cf. A047443 (numbers h such that Fibonacci(h) mod 3 = 2).

%K nonn,easy

%O 1,2

%A _N. J. A. Sloane_