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%I #18 Jun 02 2021 16:43:48
%S 5,7,13,15,15,20,23,26,31,31,39,41,41,47,49,52,57,57,62,65,68,73,75,
%T 81,83,83,89,91,94,99,99,107,109,109,115,117,123,125,125,130,133,136,
%U 141,143,149,151,151,157,159,162,167,167,172,175,178,183,185,191,193
%N Frobenius number of the lower Wythoff sequence (A000201), starting with the n-th term.
%C 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.
%C 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.
%H Jeffrey Shallit, <a href="https://arxiv.org/abs/2103.10904">Frobenius numbers and automatic sequences</a>, arXiv:2103.10904 [math.NT], 2021.
%t With[{s = Array[Floor[#*GoldenRatio] &, 120]}, Array[FrobeniusNumber[s[[# ;; -1]]] &, Floor[Length[s]/2]]] (* _Michael De Vlieger_, Jun 02 2021 *)
%Y Cf. A000201, A342716 (analog for the upper Wythoff numbers).
%K nonn
%O 2,1
%A _Jeffrey Shallit_, Mar 19 2021
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