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

0, 2, 14, 36, 38, 94, 96, 246, 248, 260, 644, 646, 658, 680, 682, 1686, 1688, 1700, 1722, 1724, 1780, 1782, 4414, 4416, 4428, 4450, 4452, 4508, 4510, 4660, 4662, 4674, 11556, 11558, 11570, 11592, 11594, 11650, 11652, 11802, 11804, 11816, 12200, 12202, 12214

Offset: 1

Author

Rémy Sigrist, Apr 23 2020

Keywords

• nonn
• base

Comments

There is a 13-state finite automaton that accepts the Zeckendorf expansions of the members of this sequence. - Jeffrey Shallit, May 03 2023

Examples

			The first terms, alongside their base phi representation, are:
  n   a(n)  phi(a(n))
  --  ----  -------------------------
   1     0             0.0
   2     2            10.01
   3    14        100100.001001
   4    36      10010000.00001001
   5    38      10010010.01001001
   6    94    1001000000.0000001001
   7    96    1001000010.0100001001
   8   246  100100000000.000000001001
   9   248  100100000010.010000001001
  10   260  100100100100.001001001001
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..1000
• Jeffrey Shallit, Proving Properties of phi-Representations with the Walnut Theorem-Prover, arXiv:2305.02672 [math.NT], 2023.
• Rémy Sigrist, PARI program for A330672
• Wikipedia, Golden ratio base

Crossrefs

See A330722 for a weaker variant.

Cf. A057148, A130600, A178482.

Programs

PARI

See Links section.

Formula

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