A348020 a(n) is the minimum number of unit resistors in a circuit with resistance R = A007305(n)/A007306(n).

1, 2, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 6, 6, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 7, 5, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8

Offset: 1

Author

Hugo Pfoertner, Oct 14 2021

Keywords

• nonn

Comments

For small values of n, the circuits are planar and correspond to the tiling of rectangles by squares. See A338573 for more information and examples.

The earliest nonplanar deviation occurs at a(3173) corresponding to R = 115/204 needing 11 instead of 12 resistors.

Links

• Hugo Pfoertner, Table of n, a(n) for n = 1..4096

Crossrefs

First 31 terms coincide with A070941.

Cf. A007305, A007306, A113881, A219158, A338573, A347282.

A338579 can be used for a lookup of the position for a given rational R.