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%I #60 Aug 05 2023 21:48:56
%S 1,3,6,8,11,14,16,19,21,24,27,29,32,35,37,40,42,45,48,50,53,55,58,61,
%T 63,66,69,71,74,76,79,82,84,87,90,92,95,97,100,103,105,108,110,113,
%U 116,118,121,124,126,129,131,134,137,139,142,144
%N a(n) = floor(n*tau) + n + 1 where tau is the golden ratio A001622.
%C a(n) = greatest k such that s(k) = n+1, where s = A026350.
%C Indices at which blocks (0;1) occur in infinite Fibonacci word; i.e., n such that A005614(n)=0 and A005614(n+1)=1. - _Benoit Cloitre_, Nov 15 2003
%C Except for the first term, these are the numbers whose lazy Fibonacci representation (see A095791) includes both 1 and 2; thus this sequence is a subsequence of the lower Wythoff sequence, A000201. - _Clark Kimberling_, Jun 10 2004 [A-number typo corrected by _Nathan Fox_, May 03 2014]
%C a(n) = n-th number k whose lazy Fibonacci representation (as in A095791) has more summands than that of k-1. - _Clark Kimberling_, Jun 12 2004
%C a(n) = position of n-th 0 in A096270. - _Clark Kimberling_, Apr 22 2011
%C Maximum number of chips in a pile created at each step in the game described by Roland Schroeder in his comment at A000201. (From _Allan C. Wechsler_ via Seqfan.)
%H Eric Friedman, Scott M. Garrabrant, Ilona K. Phipps-Morgan, A. S. Landsberg and Urban Larsson, <a href="http://library.msri.org/books/Book70/files/1015.pdf">Geometric analysis of a generalized Wythoff game</a>, in Games of no Chance 5, MSRI publ. Cambridge University Press, 2019.
%H U. Larsson and N. Fox, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Larsson/larsson8.html">An Aperiodic Subtraction Game of Nim-Dimension Two</a>, Journal of Integer Sequences, 2015, Vol. 18, #15.7.4.
%H Ali Sada, <a href="http://list.seqfan.eu/pipermail/seqfan/2023-June/074685.html">Should A000201 and A026352 be cross-referenced?</a>, Seqfan thread, Jun 2023.
%t Table[Floor[GoldenRatio*n]+n+1,{n,0,60}] (* _Harvey P. Dale_, Aug 24 2021 *)
%o (PARI) a(n) = floor(n*(sqrt(5)+1)/2) + n + 1; \\ _Michel Marcus_, Sep 15 2016
%o (Python)
%o from math import isqrt
%o def A026352(n): return (n+isqrt(5*n**2)>>1)+n+1 # _Chai Wah Wu_, Aug 25 2022
%Y Essentially same as A004957.
%Y Cf. A001622, A005614, A026350, A095791, A096270.
%Y Subsequence of A000201.
%Y Complement of A026351.
%K nonn
%O 0,2
%A _Clark Kimberling_, Dec 11 1999
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