A342581 Frobenius number of the evil numbers (A001969) starting with the n-th term.

7, 13, 14, 16, 31, 31, 31, 32, 55, 55, 55, 55, 55, 61, 62, 64, 69, 74, 81, 127, 127, 127, 127, 127, 127, 127, 127, 127, 127, 127, 127, 128, 133, 138, 145, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223, 223

Offset

3,1

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=3..57.

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

Example

For n = 4, the Frobenius number of (5, 6, 9, 10, 12, 15, ...) is 13.

Crossrefs

Cf. A001969. The analogous sequence for the odious numbers is A342579.

Sequence in context: A194408 A057930 A363491 * A353443 A332480 A233593

Adjacent sequences: A342578 A342579 A342580 * A342582 A342583 A342584

Keyword

nonn,base

Author

Jeffrey Shallit, Mar 15 2021

Status

approved