A342715 Frobenius number of the lower Wythoff sequence (A000201), starting with the n-th term.

5, 7, 13, 15, 15, 20, 23, 26, 31, 31, 39, 41, 41, 47, 49, 52, 57, 57, 62, 65, 68, 73, 75, 81, 83, 83, 89, 91, 94, 99, 99, 107, 109, 109, 115, 117, 123, 125, 125, 130, 133, 136, 141, 143, 149, 151, 151, 157, 159, 162, 167, 167, 172, 175, 178, 183, 185, 191, 193

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.

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=2..60.

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

Mathematica

With[{s = Array[Floor[#*GoldenRatio] &, 120]}, Array[FrobeniusNumber[s[[# ;; -1]]] &, Floor[Length[s]/2]]] (* Michael De Vlieger, Jun 02 2021 *)

Crossrefs

Cf. A000201, A342716 (analog for the upper Wythoff numbers).

Sequence in context: A166163 A249801 A318346 * A050079 A372081 A314313

Adjacent sequences: A342712 A342713 A342714 * A342716 A342717 A342718

Keyword

nonn

Author

Jeffrey Shallit, Mar 19 2021

Status

approved