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

1,2

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.

Sequence in context: A029128 A303660 A290021 * A070941 A061775 A356384

Adjacent sequences: A348017 A348018 A348019 * A348021 A348022 A348023

Keyword

nonn

Author

Hugo Pfoertner, Oct 14 2021

Status

approved