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A047471 Numbers that are congruent to {1, 3} mod 8.

%I A047471 #41 Sep 08 2022 08:44:57
%S A047471 1,3,9,11,17,19,25,27,33,35,41,43,49,51,57,59,65,67,73,75,81,83,89,91,
%T A047471 97,99,105,107,113,115,121,123,129,131,137,139,145,147,153,155,161,
%U A047471 163,169,171,177,179,185,187,193,195,201,203,209,211,217,219,225,227,233
%N A047471 Numbers that are congruent to {1, 3} mod 8.
%H A047471 Reinhard Zumkeller, <a href="/A047471/b047471.txt">Table of n, a(n) for n = 1..1000</a>
%H A047471 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%F A047471 G.f.: x*(1+2*x+5*x^2)/((1+x)*(1-x)^2). - _Paul Barry_, Apr 10 2008
%F A047471 a(n) = 4*(n-1)-(-1)^n. - _Rolf Pleisch_, Aug 04 2009
%F A047471 a(n) = 8*n-a(n-1)-12, with a(1)=1. - _Vincenzo Librandi_, Aug 06 2010
%F A047471 Sum_{n>=1} (-1)^(n+1)/a(n) = Pi/8 + sqrt(2)*log(sqrt(2)+1)/4. - _Amiram Eldar_, Dec 18 2021
%e A047471 For n=2, a(2) = 8*2-1-12 = 3;
%e A047471 For n=3, a(3) = 8*3-3-12 = 9;
%e A047471 For n=4, a(4) = 8*4-9-12 = 11. - _Vincenzo Librandi_, Aug 06 2010
%p A047471 A047471:=n->4*n - 4 - (-1)^n; seq(A047471(n), n=1..100); # _Wesley Ivan Hurt_, Jan 30 2014
%t A047471 Table[4 n - 4 - (-1)^n, {n, 100}] (* _Wesley Ivan Hurt_, Jan 30 2014 *)
%t A047471 #+{1,3}&/@(8*Range[0,30])//Flatten (* or *) LinearRecurrence[{1,1,-1},{1,3,9},60] (* _Harvey P. Dale_, Jan 05 2017 *)
%o A047471 (Haskell)
%o A047471 a047471 n = a047471_list !! (n-1)
%o A047471 a047471_list = [n | n <- [1..], mod n 8 `elem` [1,3]]
%o A047471 -- _Reinhard Zumkeller_, Dec 29 2012
%o A047471 (Magma) [4*(n-1)-(-1)^n : n in [1..80]]; // _Wesley Ivan Hurt_, Apr 28 2017
%Y A047471 Union of A017077 and A017101.
%Y A047471 Cf. A033200 (primes).
%K A047471 nonn,easy
%O A047471 1,2
%A A047471 _N. J. A. Sloane_
%E A047471 More terms from _Vincenzo Librandi_, Aug 06 2010