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 A173989 #30 Aug 29 2025 15:51:00
%S A173989 0,0,1,1,2,1,3,3,4,3,5,5,6,5,7,7,8,7,9,9,10,9,11,11,12,11,13,13,14,13,
%T A173989 15,15,16,15,17,17,18,17,19,19,20,19,21,21,22,21,23,23,24,23,25,25,26,
%U A173989 25,27,27,28,27,29,29,30,29,31,31,32,31,33,33,34,33,35,35,36,35,37,37,38,37
%N A173989 a(n) is the 2-adic valuation of A173300(n).
%C A173989 Conjecture: always follows the pattern A, A, A+1, A, where A is an odd number.
%H A173989 Hugo Pfoertner, <a href="/A173989/b173989.txt">Table of n, a(n) for n = 1..1000</a>
%F A173989 a(n) = log(A173300(n))/log(2).
%F A173989 Apparently a(n) = A102302(n) for n >= 7. - _Hugo Pfoertner_, Oct 10 2018
%F A173989 Conjectures from _Colin Barker_, Oct 10 2018: (Start)
%F A173989 G.f.: x^3*(1 + x^2 - x^3 + x^4) / ((1 - x)^2*(1 + x)*(1 + x^2)).
%F A173989 a(n) = a(n-1) + a(n-4) - a(n-5) for n > 7.
%F A173989 (End)
%F A173989 Apparently a(n) = A116921(n) for n>=3. - _R. J. Mathar_, Aug 29 2025
%p A173989 From _R. J. Mathar_, Mar 20 2010: (Start)
%p A173989 A173300 := proc(n) local x,y ; x := (1+sqrt(3))/2 ; y := (1-sqrt(3))/2 ; denom(expand(x^n+y^n)) ; end proc:
%p A173989 A173989 := proc(n) log[2](A173300(n)) ; end proc: seq(A173989(n),n=3..100) ; (End)
%t A173989 Log2[Denominator[Map[First, NestList[{Last[#], Last[#] + First[#]/2} &, {1, 2}, 100]]]] (* Paolo Xausa, Feb 01 2024, after _Nick Hobson_ in A173300 *)
%o A173989 (PARI) \\ using _Max Alekseyev_'s function in A173300
%o A173989 A173300(n) = denominator(2*polcoeff( lift( Mod((1+x)/2, x^2-3)^n ), 0))
%o A173989 for(k=1,74,print1(logint(A173300(k),2),", ")) \\ _Hugo Pfoertner_, Oct 10 2018
%Y A173989 Cf. A102302, A173300.
%K A173989 nonn,changed
%O A173989 1,5
%A A173989 _J. Lowell_, Mar 04 2010
%E A173989 More terms from _R. J. Mathar_ and _Max Alekseyev_, Mar 20 2010