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A362781 Natural numbers n for which some base-phi representation of n is anti-palindromic.

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%I A362781 #14 May 05 2023 01:36:24
%S A362781 0,1,3,4,5,6,8,11,13,14,15,16,21,23,29,31,33,35,37,39,41,43,45,53,55,
%T A362781 61,63,76,78,80,86,88,89,91,97,99,100,102,108,110,111,113,119,121,136,
%U A362781 138,144,146,158,160,166,168,199,201,203,209,211,223,225,230,231
%N A362781 Natural numbers n for which some base-phi representation of n is anti-palindromic.
%C A362781 Here "anti-palindromic" means the expansion is of the form x.y, where the complement of y is the reverse of x (allowing leading or trailing zeros).  Here we do not insist that the base-phi representation be "canonical" (that is, we do not insist that xy contains no 11).
%H A362781 George Bergman, <a href="https://www.jstor.org/stable/3029218">A number system with an irrational base</a>, Math. Mag. 31 (1957), pp. 98-110.
%H A362781 Jeffrey Shallit, <a href="https://arxiv.org/abs/2305.02672">Proving Properties of phi-Representations with the Walnut Theorem-Prover</a>, arXiv:2305.02672 [math.NT], 2023.
%F A362781 There is a 193-state automaton accepting the Zeckendorf representation of the members of this sequence.
%e A362781 For example, one base-phi representation of 13 is 00100001.01111011.
%Y A362781 Cf. A105424, A341722.
%K A362781 nonn,base
%O A362781 1,3
%A A362781 _Jeffrey Shallit_, May 03 2023