A362780 Numbers n having some (possibly non-canonical) base-phi representation x.y, where y is the reverse of x.

0, 2, 6, 14, 36, 38, 94, 96, 100, 246, 248, 252, 260, 644, 646, 650, 658, 680, 682, 1686, 1688, 1692, 1700, 1722, 1724, 1780, 1782, 1786, 4414, 4416, 4420, 4428, 4450, 4452, 4508, 4510, 4514, 4660, 4662, 4666, 4674, 11556, 11558, 11562, 11570, 11592, 11594

Offset: 1

Author

Jeffrey Shallit, May 03 2023

Keywords

• nonn
• base

Comments

Similar to A330672, but including those n with non-canonical representation (i.e., allowing 11 to be present) having the desired property. For example, 6 has representation 1001.1001.

Links

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

Crossrefs

Cf. A330672.