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

Author

Jeffrey Shallit, Mar 19 2021

Keywords

• nonn

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

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

Crossrefs

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