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

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, 61, 63, 76, 78, 80, 86, 88, 89, 91, 97, 99, 100, 102, 108, 110, 111, 113, 119, 121, 136, 138, 144, 146, 158, 160, 166, 168, 199, 201, 203, 209, 211, 223, 225, 230, 231

Offset: 1

Author

Jeffrey Shallit, May 03 2023

Keywords

• nonn
• base

Comments

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).

Examples

			For example, one base-phi representation of 13 is 00100001.01111011.
		

Links

• George Bergman, A number system with an irrational base, Math. Mag. 31 (1957), pp. 98-110.
• Jeffrey Shallit, Proving Properties of phi-Representations with the Walnut Theorem-Prover, arXiv:2305.02672 [math.NT], 2023.

Crossrefs

Cf. A105424, A341722.

Formula

There is a 193-state automaton accepting the Zeckendorf representation of the members of this sequence.