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A176499 Haros-Farey Sequence whose argument is the Fibonacci Number; Farey(m) where m = Fibonacci (n + 1). 13
2, 3, 5, 11, 23, 59, 141, 361, 941, 2457, 6331, 16619, 43359, 113159, 296385, 775897, 2030103, 5315385, 13912615, 36421835, 95355147, 249635525, 653525857, 1710966825, 4479358275, 11726974249, 30701593527, 80377757397, 210431301141 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This sequence arises in the analytically obtained strict upper bound of the set of equivalent resistances formed by any conceivable network (series/parallel or bridge, or non-planar) of n equal resistors. Consequently it provides a strict upper bound of the sequences: A048211, A153588, A174283, A174284, A174285 and A174286. A better strict bound is obtained by the Sequence A176501, but it is difficult to compute due to memory limitations.

Farey(n) = A005728(n). [From Franklin T. Adams-Watters, May 12 2010]

REFERENCES

Antoni Amengual, The intriguing properties of the equivalent resistances of n equal resistors combined in series and in parallel, American Journal of Physics, 68(2), 175-179 (February 2000). Digital Object Identifier (DOI): http://dx.doi.org/10.1119/1.19396

LINKS

Table of n, a(n) for n=1..29.

Sameen Ahmed Khan, The bounds of the set of equivalent resistances of n equal resistors combined in series and in parallel, arXiv:1004.3346v1 [physics.gen-ph], (20 April 2010).

Sameen Ahmed KHAN, Mathematica notebook 1

Sameen Ahmed KHAN, Mathematica notebook 2

EXAMPLE

n = 5, m = Fibonacci(5 + 1) = 8, Farey(8) = 23.

CROSSREFS

Cf. A048211, A153588, A174283, A174284, A174285 and A174286, A176500, A176501, A176502

Sequence in context: A027763 A233694 A261810 * A175234 A060696 A076051

Adjacent sequences:  A176496 A176497 A176498 * A176500 A176501 A176502

KEYWORD

nonn

AUTHOR

Sameen Ahmed Khan, Apr 21 2010

EXTENSIONS

Added four terms: 26 to 29. Sameen Ahmed Khan, May 02 2010

STATUS

approved

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Last modified August 21 17:39 EDT 2017. Contains 290891 sequences.