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

1,2

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

Table of n, a(n) for n=1..47.

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.

Sequence in context: A318018 A025257 A283438 * A323027 A110152 A245560

Adjacent sequences: A362777 A362778 A362779 * A362781 A362782 A362783

Keyword

nonn,base

Author

Jeffrey Shallit, May 03 2023

Status

approved