A342716 Frobenius number of the upper Wythoff sequence (A001950), starting with the n-th term.

3, 16, 19, 42, 42, 42, 55, 58, 76, 79, 79, 110, 110, 110, 118, 121, 144, 144, 144, 155, 160, 173, 181, 181, 207, 207, 207, 220, 223, 254, 254, 254, 275, 275, 275, 283, 283, 309, 309, 309, 320, 325, 343, 346, 346, 377, 377, 377, 385, 388, 406, 409, 409, 422

Offset

1,1

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.

The sequence a(n) is "Fibonacci-synchronized"; there is an automaton that recognizes the Fibonacci representation of the pairs (n, a(n)) in parallel. This means specific values of a(n) are easily computed.

Links

Table of n, a(n) for n=1..54.

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

Crossrefs

Cf. A001950, A342715 (analog for the lower Wythoff numbers).

Sequence in context: A022126 A127006 A042075 * A042777 A041461 A277724

Adjacent sequences: A342713 A342714 A342715 * A342717 A342718 A342719

Keyword

nonn

Author

Jeffrey Shallit, Mar 19 2021

Status

approved