

A073334


The socalled "rhythmic infinity system" of Danish composer Per Nørgård [Noergaard].


2



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
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OFFSET

0,1


COMMENTS

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


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. 7193.


LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000
J.P. Allouche and J. Shallit, The ring of kregular sequences, II, Theoret. Computer Sci., 307 (2003), 329.
J.P. Allouche and J. Shallit, The Ring of kregular Sequences, II
Jeffrey Shallit, The mathematics of Per Noergaard's rhythmic infinity system, Fib. Q., 43 (2005), 262268.


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


EXAMPLE

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.


MATHEMATICA

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


PROG

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


CROSSREFS

Cf. A005811, A000045.
Sequence in context: A152304 A021902 A136188 * A021740 A172370 A304026
Adjacent sequences: A073331 A073332 A073333 * A073335 A073336 A073337


KEYWORD

nonn,hear


AUTHOR

Jeffrey Shallit, Aug 25 2002


STATUS

approved



