A330672 - OEIS

%I #31 May 05 2023 01:35:47

%S 0,2,14,36,38,94,96,246,248,260,644,646,658,680,682,1686,1688,1700,

%T 1722,1724,1780,1782,4414,4416,4428,4450,4452,4508,4510,4660,4662,

%U 4674,11556,11558,11570,11592,11594,11650,11652,11802,11804,11816,12200,12202,12214

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

%C There is a 13-state finite automaton that accepts the Zeckendorf expansions of the members of this sequence. - _Jeffrey Shallit_, May 03 2023

%H Rémy Sigrist, <a href="/A330672/b330672.txt">Table of n, a(n) for n = 1..1000</a>

%H 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 Rémy Sigrist, <a href="/A330672/a330672.gp.txt">PARI program for A330672</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Golden_ratio_base">Golden ratio base</a>

%F A130600(a(n)) belongs to A057148 for any n >= 0.

%e The first terms, alongside their base phi representation, are:

%e   n   a(n)  phi(a(n))

%e   --  ----  -------------------------

%e    1     0             0.0

%e    2     2            10.01

%e    3    14        100100.001001

%e    4    36      10010000.00001001

%e    5    38      10010010.01001001

%e    6    94    1001000000.0000001001

%e    7    96    1001000010.0100001001

%e    8   246  100100000000.000000001001

%e    9   248  100100000010.010000001001

%e   10   260  100100100100.001001001001

%o (PARI) See Links section.

%Y See A330722 for a weaker variant.

%Y Cf. A057148, A130600, A178482.

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Apr 23 2020