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

1,2

Comments

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

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

Formula

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

Example

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

Prog

(PARI) See Links section.

Crossrefs

See A330722 for a weaker variant.

Cf. A057148, A130600, A178482.

Sequence in context: A367578 A134647 A004117 * A135706 A091520 A338327

Adjacent sequences: A330669 A330670 A330671 * A330673 A330674 A330675

Keyword

nonn,base

Author

Rémy Sigrist, Apr 23 2020

Status

approved