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 A060144 #68 Jul 29 2025 15:35:50
%S A060144 0,0,0,1,1,1,2,2,3,3,3,4,4,4,5,5,6,6,6,7,7,8,8,8,9,9,9,10,10,11,11,11,
%T A060144 12,12,12,13,13,14,14,14,15,15,16,16,16,17,17,17,18,18,19,19,19,20,20,
%U A060144 21,21,21,22,22,22,23,23,24,24,24,25,25,25,26,26,27,27,27,28,28,29,29
%N A060144 a(n) = floor(n/(1+tau)), or equivalently floor(n/(tau)^2), where tau is the golden ratio (A001622).
%C A060144 The RUNS transform of this sequence appears to be yet another version of the Fibonacci word (cf. A001468, A001950, A076662). - _N. J. A. Sloane_, Mar 29 2025
%H A060144 Harry J. Smith, <a href="/A060144/b060144.txt">Table of n, a(n) for n = 0..1000</a>
%H A060144 Martin Griffiths, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Papers1/56-1/GriffithsmgFibWordSeq121517.pdf">A formula for an infinite family of Fibonacci-word sequences</a>, Fib. Q., 56 (2018), 75-80.
%H A060144 D. R. Hofstadter, <a href="/A006336/a006336_1.pdf">Eta-Lore</a> [With permission]
%H A060144 D. R. Hofstadter, <a href="/A006336/a006336_2.pdf">Pi-Mu Sequences</a> [With permission]
%H A060144 D. R. Hofstadter and N. J. A. Sloane, <a href="/A006336/a006336.pdf">Correspondence, 1977 and 1991</a> (On page 4 of DRH letter, v[n] = A006336, a[n] = A060144[n+1]). - _N. J. A. Sloane_, Oct 25 2014
%H A060144 Johan Kok, <a href="https://arxiv.org/abs/2507.16500">Integer sequences with conjectured relation with certain graph parameters of the family of linear Jaco graphs</a>, arXiv:2507.16500 [math.CO], 2025. See p. 4.
%F A060144 For n>0, a(n)=n reduced modulo A005206(n). - _Benoit Cloitre_, Jan 01 2003
%F A060144 Let n' = n-1. Above formula is better as a(n') = n'-A005206(n'). Also a(n') = A005206(A005206(n'-1)). Also a(n'+1) = n'-a(n')-a(n'-a(n')), with a(0) = 0. - _Frank Ruskey_, Dec 09 2011
%F A060144 a(n+1) = n - A005206(n). - _Reinhard Zumkeller_, Apr 07 2012
%F A060144 a(n) = floor(n*A132338). - _R. J. Mathar_, Jul 29 2021
%p A060144 A060144 := proc(n)
%p A060144 (3+sqrt(5))/2 ;
%p A060144 floor(n/%) ;
%p A060144 end proc:
%p A060144 seq(A060144(n),n=0..100) ; # _R. J. Mathar_, Jul 29 2021
%t A060144 Table[Floor[n/GoldenRatio^2], {n, 0, 100}] (* _T. D. Noe_, Dec 10 2011 *)
%o A060144 (PARI)
%o A060144 { default(realprecision, 10); f=2/(sqrt(5) + 3); for (n=0, 1000, write("b060144.txt", n, " ", floor(n*f)); ) } \\ _Harry J. Smith_, Jul 02 2009
%o A060144 (Haskell)
%o A060144 a060144 n = a060144_list !! n
%o A060144 a060144_list = 0 : 0 : scanl1 (+) a003849_list
%o A060144 -- _Reinhard Zumkeller_, Apr 07 2012
%o A060144 (Python)
%o A060144 from math import isqrt
%o A060144 def A060144(n): return (n<<1)-1-(n+isqrt(5*n**2)>>1) if n else 0 # _Chai Wah Wu_, Aug 09 2022
%Y A060144 Cf. A001622, A005206, A006336.
%Y A060144 See also A001468, A001950, A076662.
%K A060144 nonn
%O A060144 0,7
%A A060144 _Clark Kimberling_, Mar 05 2001