|
%I #26 Mar 11 2016 09:12:15
%S 3,5,8,5,8,13,8,5,8,13,21,13,8,13,8,5,8,13,21,13,21,34,21,13,8,13,21,
%T 13,8,13,8,5,8,13,21,13,21,34,21,13,21,34,55,34,21,34,21,13,8,13,21,
%U 13,21,34,21,13,8,13,21,13,8,13,8,5,8,13,21,13,21,34,21,13,21,34,55,34,21
%N The so-called "rhythmic infinity system" of Danish composer Per Nørgård [Noergaard].
%C The composer Per Nørgård's name is also written in the OEIS as Per Noergaard.
%D Erling Kullberg, Beyond infinity: on the infinity series - the DNA of hierarchical music, in Anders Beyer, ed., The Music of Per Noergaard: Fourteen Interpretive Essays, Scolar Press, 1996, pp. 71-93.
%H Reinhard Zumkeller, <a href="/A073334/b073334.txt">Table of n, a(n) for n = 0..10000</a>
%H J.-P. Allouche and J. Shallit, <a href="http://dx.doi.org/10.1016/S0304-3975(03)00090-2">The ring of k-regular sequences, II</a>, Theoret. Computer Sci., 307 (2003), 3-29.
%H J.-P. Allouche and J. Shallit, <a href="http://www.math.jussieu.fr/~allouche/kreg2.ps">The Ring of k-regular Sequences, II</a>
%H Jeffrey Shallit, <a href="http://www.fq.math.ca/Papers1/43-3/paper43-3-9.pdf">The mathematics of Per Noergaard's rhythmic infinity system</a>, Fib. Q., 43 (2005), 262-268.
%F a(n) = F(c(n)+4) where c(n) counts the blocks of consecutive identical symbols in the binary expansion of n and F() is the Fibonacci sequence.
%F a(n) = A000045(A005811(n)+4) for n > 0. - _Reinhard Zumkeller_, May 23 2013
%e a(5) = 13 since there are 3 blocks of consecutive identical systems in the binary expansion of 5 (namely, 101), 4+3 = 7 and the 7th Fibonacci number is 13.
%t {3}~Join~Table[Fibonacci[Length@ Split@ IntegerDigits[n, 2] + 4], {n, 76}] (* _Michael De Vlieger_, Mar 10 2016 *)
%o (Haskell)
%o a073334 0 = 3
%o a073334 n = a000045 $ a005811 n + 4 -- _Reinhard Zumkeller_, May 23 2013
%Y Cf. A005811, A000045.
%K nonn,hear
%O 0,1
%A _Jeffrey Shallit_, Aug 25 2002
|
