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 A350666 #22 Mar 06 2022 08:30:02
%S A350666 0,5,7,9,14,16,18,23,25,27,32,34,36,41,43,45,50,52,54,59,61,63,68,70,
%T A350666 72,77,79,81,86,88,90,95,97,99,104,106,108,113,115,117,122,124,126,
%U A350666 131,133,135,140,142,144,149
%N A350666 Numbers congruent to 0, 5, and 7 modulo 9: positions of 0 in A159955.
%C A350666 This sequence, together with A350667 and A350668, gives a 3-set partition of the nonnegative integers.
%C A350666 This sequence {a(n)}, for n >= 1, gives the indices of the row sequences of array A = A347834, that are modulo 6 periodic with period length 3, namely: {A347834(a(n), m) mod 6}_{m >= 0} = {repeat(0, 3, 1)}.
%H A350666 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (1,0,1,-1).
%F A350666 A159955(a(n)) = 0.
%F A350666 Trisection: a(3*k) = 9*k, a(3*k+1) = 5 + 9*k, and a(3*k+2) = 7 + 9*k, for k >= 0.
%F A350666 G.f.: x*(5 + 2*x + 2*x^2)/((1 - x)*(1 - x^3)).
%F A350666 a(n) = 1 + 3*n - U(n, -1/2) = 1+3*n-A049347(n), where U(n, x) is a Chebyshev U-polynomial. - _Stefano Spezia_, Jan 30 2022
%F A350666 a(n) = 1 + 3*n - (2/sqrt(3))*sin(2*(n+1)*Pi/3) (from the previous formula).
%e A350666 Rows of array {A347834(a(n), m)}_{m>=0}, with modulo 6 congruence:
%e A350666 n = 1: row 5: {11, 45, 181, 725, 2901, 11605,...} mod 6 = {5, 3, 1, 5, 3, 1, ...},
%e A350666 n = 2: row 7: {17, 69, 277, 1109, 4437, 17749, ...} mod 6 = {repeat(5, 3, 1)},
%e A350666 ...
%t A350666 Select[Range[0, 150], MemberQ[{0, 5, 7}, Mod[#, 9]] &] (* _Amiram Eldar_, Jan 29 2022 *)
%t A350666 Table[1 + 3n - ChebyshevU[n,-1/2],{n,0,49}] (* _Stefano Spezia_, Jan 30 2022 *)
%Y A350666 Cf. A159955, A347834, A350667, A350668.
%K A350666 nonn,easy
%O A350666 0,2
%A A350666 _Wolfdieter Lang_, Jan 29 2022