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Floor(n*beta)-1, where 1/alpha+1/beta=1, alpha being the number with continued fraction expansion [1;1,2,3,4,5,...] (A247844).
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%I #9 May 23 2018 08:10:25

%S 1,3,6,8,11,13,16,18,20,23,25,28,30,33,35,37,40,42,45,47,50,52,54,57,

%T 59,62,64,67,69,71,74,76,79,81,84,86,89,91,93,96,98,101,103,106,108,

%U 110,113,115,118,120,123,125,127,130,132,135,137,140,142,144,147,149,152,154,157,159,162,164,166,169,171,174,176

%N Floor(n*beta)-1, where 1/alpha+1/beta=1, alpha being the number with continued fraction expansion [1;1,2,3,4,5,...] (A247844).

%H L. Goldberg and A. V. Fraenkel, <a href="http://www.wisdom.weizmann.ac.il/~fraenkel/Papers/Patterns.pdf">Patterns in the generalized Fibonacci word, applied to games</a>, Discrete Math., 341 2018 1675-1687.

%Y Cf. A247844.

%Y Complement of A303589.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, May 23 2018