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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, 550916379293 (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). [Franklin T. Adams-Watters, May 12 2010]

LINKS

Antoine Mathys, Table of n, a(n) for n = 1..49

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): 10.1119/1.19396.

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

FORMULA

a(n) = A005728(A000045(n+1)). - Michel Marcus, Jul 31 2018

EXAMPLE

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

MAPLE

with(numtheory): with(combinat, fibonacci): a:=n->1+add(phi(i), i=1..n): seq(a(fibonacci(n+1)), n=1..30); # Muniru A Asiru, Jul 31 2018

MATHEMATICA

b[n_] := 1 + Sum[EulerPhi[i], {i, 1, n}];

a[n_] := b[Fibonacci[n + 1]];

Array[a, 30] (* Jean-Fran├žois Alcover, Sep 20 2018 *)

PROG

(PARI) farey(n) = 1+sum(k=1, n, eulerphi(k));

a(n) = farey(fibonacci(n+1)); \\ Michel Marcus, Jul 31 2018

List([1..30], n->Sum([1..Fibonacci(n+1)], i->Phi(i)))+1; # Muniru A Asiru, Jul 31 2018

CROSSREFS

Cf. A000045, A005728.

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

a(26)-a(29) from Sameen Ahmed Khan, May 02 2010

a(30) from Antoine Mathys, Aug 06 2018

STATUS

approved

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Last modified October 23 22:04 EDT 2018. Contains 316541 sequences. (Running on oeis4.)