A073334 The so-called "rhythmic infinity system" of Danish composer Per Nørgård [Noergaard].

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, 13, 8, 13, 8, 5, 8, 13, 21, 13, 21, 34, 21, 13, 21, 34, 55, 34, 21, 34, 21, 13, 8, 13, 21, 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

Offset: 0

Author

Jeffrey Shallit, Aug 25 2002

Keywords

• nonn
• hear

Comments

The composer Per Nørgård's name is also written in the OEIS as Per Noergaard.

Examples

			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.
		

References

• 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.

Links

• Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
• J.-P. Allouche and J. Shallit, The ring of k-regular sequences, II, Theoret. Computer Sci., 307 (2003), 3-29.
• J.-P. Allouche and J. Shallit, The Ring of k-regular Sequences, II
• Jeffrey Shallit, The mathematics of Per Noergaard's rhythmic infinity system, Fib. Q., 43 (2005), 262-268.

Crossrefs

Cf. A005811, A000045.

Programs

Haskell

a073334 0 = 3
a073334 n = a000045 $ a005811 n + 4  -- Reinhard Zumkeller, May 23 2013

Mathematica

{3}~Join~Table[Fibonacci[Length@ Split@ IntegerDigits[n, 2] + 4], {n, 76}] (* Michael De Vlieger, Mar 10 2016 *)

Formula

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.

a(n) = A000045(A005811(n)+4) for n > 0. - Reinhard Zumkeller, May 23 2013