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A249031 The non-anti-Fibonacci numbers: numbers not in A075326.

%I A249031 #29 Jun 23 2025 10:54:30
%S A249031 1,2,4,5,6,7,8,10,11,12,14,15,16,17,19,20,21,22,24,25,26,27,28,30,31,
%T A249031 32,34,35,36,37,38,40,41,42,44,45,46,47,48,50,51,52,54,55,56,57,59,60,
%U A249031 61,62,64,65,66,67,68,70,71,72,74,75,76,77,79,80,81,82,84,85,86,87,88,90,91,92,94,95,96,97,99,100
%N A249031 The non-anti-Fibonacci numbers: numbers not in A075326.
%H A249031 Reinhard Zumkeller, <a href="/A249031/b249031.txt">Table of n, a(n) for n = 1..10000</a>
%H A249031 Wieb Bosma, Rene Bruin, Robbert Fokkink, Jonathan Grube, Anniek Reuijl, and Thian Tromp, <a href="https://arxiv.org/abs/2503.04122">Using Walnut to solve problems from the OEIS</a>, arXiv:2503.04122 [math.NT], 2025. See p. 7.
%H A249031 Robbert Fokkink and Gandhar Joshi, <a href="https://arxiv.org/abs/2506.13337">Anti-recurrence sequences</a>, arXiv:2506.13337 [math.NT], 2025. See p. 4.
%H A249031 D. R. Hofstadter, <a href="/A075326/a075326_1.pdf">Anti-Fibonacci numbers</a>, Oct 23 2014
%H A249031 Thomas Zaslavsky, <a href="/A075326/a075326_2.pdf">Anti-Fibonacci Numbers: A Formula</a>, Sep 26 2016
%o A249031 (Haskell)
%o A249031 import Data.List ((\\))
%o A249031 a249031 n = a249031_list !! (n-1)
%o A249031 a249031_list = f [1..] where
%o A249031    f ws@(u:v:_) = u : v : f (ws \\ [u, v, u + v])
%o A249031 -- _Reinhard Zumkeller_, Oct 26 2014
%o A249031 (Python)
%o A249031 def A249031(n): return n+(n+1-(m:=n-3&7)>>2)+int(m>=4 and (m!=4 or (~((k:=n-3>>3)+1)&k).bit_length()&1)) # _Chai Wah Wu_, Sep 11 2024
%Y A249031 Cf. A075326, A249032.
%K A249031 nonn
%O A249031 1,2
%A A249031 _N. J. A. Sloane_, Oct 26 2014