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A007064 Numbers not of form "nearest integer to n*tau", tau = (1+sqrt(5))/2.

%I A007064 M3298 #46 Feb 12 2025 09:31:31
%S A007064 1,4,7,9,12,14,17,20,22,25,27,30,33,35,38,41,43,46,48,51,54,56,59,62,
%T A007064 64,67,69,72,75,77,80,82,85,88,90,93,96,98,101,103,106,109,111,114,
%U A007064 117,119,122,124,127,130,132,135
%N A007064 Numbers not of form "nearest integer to n*tau", tau = (1+sqrt(5))/2.
%C A007064 First column of Stolarsky array.
%C A007064 This sequence and A057843 are very similar - this can be seen if the terms equal to 4 are aligned. - _Thomas Baruchel_, Nov 04 2003
%D A007064 Clark Kimberling, "Stolarsky interspersions," Ars Combinatoria 39 (1995) 129-138.
%D A007064 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H A007064 Vincenzo Librandi, <a href="/A007064/b007064.txt">Table of n, a(n) for n = 1..1000</a>
%H A007064 Benoit Cloitre and Jeffrey Shallit, <a href="https://arxiv.org/abs/2312.11706">Some Fibonacci-Related Sequences</a>, arXiv:2312.11706 [math.CO], 2023.
%H A007064 Clark Kimberling, <a href="http://faculty.evansville.edu/ck6/integer/intersp.html">Interspersions</a>
%H A007064 Clark Kimberling, <a href="https://doi.org/10.1090/S0002-9939-1993-1111434-0">Interspersions and dispersions</a>, Proceedings of the American Mathematical Society 117 (1993) 313-321.
%H A007064 N. J. A. Sloane, <a href="/classic.html#WYTH">Classic Sequences</a>
%H A007064 K. B. Stolarsky, <a href="https://web.archive.org/web/2024*/https://www.fq.math.ca/Scanned/15-3/stolarsky.pdf">A set of generalized Fibonacci sequences such that each natural number belongs to exactly one</a>, Fib. Quart., 15 (1977), 224.
%F A007064 a(n) = floor[n*(1+tau)-tau/2] =floor[n*2.6180...-0.8090...]. - _Henry Bottomley_, Sep 03 2001
%t A007064 max = 100; Complement[ Range[ max*GoldenRatio], Round[ Range[max]*GoldenRatio]] (* _Jean-François Alcover_, Oct 10 2011 *)
%o A007064 (PARI) a(n) = tau=(1+sqrt(5))/2; floor(n*(1+tau) - tau/2) \\ _Michel Marcus_, May 21 2013
%o A007064 (Python)
%o A007064 from math import isqrt
%o A007064 def A007064(n): return (6*n-1+isqrt(5*((n<<1)-1)**2))>>2 # _Chai Wah Wu_, Feb 11 2025
%Y A007064 Complement of A007067.
%Y A007064 Cf. A001622, A035506.
%K A007064 nonn,easy,nice
%O A007064 1,2
%A A007064 _N. J. A. Sloane_, _Mira Bernstein_