A342579 Frobenius number of the odious numbers (A000069) starting with the n-th term.

5, 10, 17, 23, 23, 24, 34, 39, 39, 45, 46, 71, 71, 71, 71, 95, 95, 95, 95, 95, 95, 95, 95, 96, 101, 106, 113, 119, 119, 120, 130, 159, 159, 159, 159, 159, 159, 159, 159, 183, 183, 183, 183, 183, 183, 189, 190, 287, 287, 287, 287, 287, 287, 287, 287, 287

Offset

2,1

Comments

The Frobenius number of a set S is the largest positive integer t such that t cannot be written as a nonnegative integer linear combination of the elements of S.

This sequence is 2-synchronized; there is a deterministic finite automaton accepting both n and a(n) in parallel, expressed in base 2. From this, values of the sequence at certain special values (e.g., powers of 2) are easily computed.

Links

Table of n, a(n) for n=2..57.

Jeffrey Shallit, Frobenius numbers and automatic sequences, arXiv:2103.10904 [math.NT], 2021.

Example

For n = 3, the Frobenius number of (4, 7, 8, 11, 13, ...) is 10.

Crossrefs

Cf. A000069. The analogous sequence for the evil numbers is A342581.

Sequence in context: A356182 A098022 A190550 * A313983 A313984 A313985

Adjacent sequences: A342576 A342577 A342578 * A342580 A342581 A342582

Keyword

nonn,base

Author

Jeffrey Shallit, Mar 15 2021

Status

approved