cp's OEIS Frontend

A330672 Numbers whose base phi representation is symmetrical with respect to the radix point.

%I A330672 #31 May 05 2023 01:35:47
%S A330672 0,2,14,36,38,94,96,246,248,260,644,646,658,680,682,1686,1688,1700,
%T A330672 1722,1724,1780,1782,4414,4416,4428,4450,4452,4508,4510,4660,4662,
%U A330672 4674,11556,11558,11570,11592,11594,11650,11652,11802,11804,11816,12200,12202,12214
%N A330672 Numbers whose base phi representation is symmetrical with respect to the radix point.
%C A330672 There is a 13-state finite automaton that accepts the Zeckendorf expansions of the members of this sequence. - _Jeffrey Shallit_, May 03 2023
%H A330672 Rémy Sigrist, <a href="/A330672/b330672.txt">Table of n, a(n) for n = 1..1000</a>
%H A330672 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.
%H A330672 Rémy Sigrist, <a href="/A330672/a330672.gp.txt">PARI program for A330672</a>
%H A330672 Wikipedia, <a href="https://en.wikipedia.org/wiki/Golden_ratio_base">Golden ratio base</a>
%F A330672 A130600(a(n)) belongs to A057148 for any n >= 0.
%e A330672 The first terms, alongside their base phi representation, are:
%e A330672   n   a(n)  phi(a(n))
%e A330672   --  ----  -------------------------
%e A330672    1     0             0.0
%e A330672    2     2            10.01
%e A330672    3    14        100100.001001
%e A330672    4    36      10010000.00001001
%e A330672    5    38      10010010.01001001
%e A330672    6    94    1001000000.0000001001
%e A330672    7    96    1001000010.0100001001
%e A330672    8   246  100100000000.000000001001
%e A330672    9   248  100100000010.010000001001
%e A330672   10   260  100100100100.001001001001
%o A330672 (PARI) See Links section.
%Y A330672 See A330722 for a weaker variant.
%Y A330672 Cf. A057148, A130600, A178482.
%K A330672 nonn,base
%O A330672 1,2
%A A330672 _Rémy Sigrist_, Apr 23 2020