This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A004772 #93 Mar 04 2025 15:29:53
%S A004772 0,2,3,4,6,7,8,10,11,12,14,15,16,18,19,20,22,23,24,26,27,28,30,31,32,
%T A004772 34,35,36,38,39,40,42,43,44,46,47,48,50,51,52,54,55,56,58,59,60,62,63,
%U A004772 64,66,67,68,70,71,72,74,75,76,78,79,80,82,83,84,86,87,88,90
%N A004772 Numbers that are not congruent to 1 (mod 4).
%C A004772 Numbers whose binary expansion does not end in 01.
%C A004772 Equals partial sums of 0 together with 2, 1, 1, 2, 1, 1, ... (repeated, that is A131534 without the first term). - _Bruno Berselli_, Dec 06 2016
%C A004772 It seems that the numbers m = 3*(a(n)+1)= 1, 7, 10, 13, 19, 22, 25, 31, 34 ... are exactly the indices of Fibonacci numbers F_m that start 5 consecutive pairwise coprime F_m, F_{m+1}, ..., F_{m+4}. E.g. for m=13 the numbers {233,377,610,987,1597} are coprime. - _R. J. Mathar_, Mar 04 2025
%H A004772 Vincenzo Librandi, <a href="/A004772/b004772.txt">Table of n, a(n) for n = 1..1000</a>
%H A004772 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A004772 G.f.: x^2*(2 + x + x^2)/((1 + x + x^2)*(x - 1)^2). - _R. J. Mathar_, Oct 08 2011
%F A004772 a(n) = floor((4*n-2)/3). - _Gary Detlefs_, Jan 02 2012
%F A004772 a(n) = n + ceiling((n-1)/3) - 1. - _Arkadiusz Wesolowski_, Sep 18 2012
%F A004772 From _Ant King_, Oct 19 2012: (Start)
%F A004772 a(n) = 4 + a(n-3).
%F A004772 a(n) = (12*n -9 - 3*cos(2*(n-1)*Pi/3) + sqrt(3)*sin(2*(n-1)*Pi/3))/9. (End)
%F A004772 a(n) = ceiling(4*(n-1)/3). - _Jean-François Alcover_, Mar 07 2014
%F A004772 Sum_{n>=2} (-1)^n/a(n) = log(sqrt(2)+2)/(2*sqrt(2)) + (2-sqrt(2))*log(2)/8 - (sqrt(2)-1)*Pi/8. - _Amiram Eldar_, Dec 05 2021
%F A004772 a(n) = A042965(n+1)-1. - _R. J. Mathar_, Mar 04 2025
%p A004772 seq(seq(4*i+j,j=[0,2,3]),i=0..100); # _Robert Israel_, Sep 01 2015
%t A004772 LinearRecurrence[{1,0,1,-1},{0,2,3,4},68] (* _Ant King_, Oct 19 2012 *)
%t A004772 DeleteCases[Range[0,90],_?(Mod[#,4]==1&)] (* _Harvey P. Dale_, Jun 11 2013 *)
%t A004772 CoefficientList[Series[x (2 + x + x^2)/((1 + x + x^2) (x - 1)^2), {x, 0, 100}], x] (* _Vincenzo Librandi_, Mar 08 2014 *)
%o A004772 (Magma) [n: n in [0..100] | not n mod 4 eq 1 ]; // _Vincenzo Librandi_, Mar 09 2014
%o A004772 (Magma) [(4*n-2) div 3: n in [1..100]]; // _Bruno Berselli_, Dec 06 2016
%o A004772 (PARI) a(n) = (4*n-2)\3; \\ _Michel Marcus_, Sep 03 2015
%Y A004772 Cf. A016813 (complement), A042965, A131534.
%K A004772 nonn,easy
%O A004772 1,2
%A A004772 _N. J. A. Sloane_
%E A004772 Corrected by _Michael Somos_, Jun 08 2000