A344145 Positive numbers m such that A020330^k(m) belongs to A344022 for any k >= 0 (where f^k denotes the k-th iterate of f).

2, 9, 10, 12, 35, 37, 38, 41, 42, 44, 49, 50, 52, 56, 139, 141, 142, 147, 149, 150, 153, 154, 156, 163, 165, 166, 169, 170, 172, 177, 178, 180, 184, 197, 198, 201, 202, 204, 209, 210, 212, 216, 226, 228, 232, 555, 557, 558, 563, 565, 566, 569, 570, 587, 589

Offset: 1

Author

Rémy Sigrist, May 10 2021

Keywords

• nonn
• base

Comments

The binary expansion of a term, say (b_1, ..., b_m), encodes an m-periodic nonintersecting infinite walk made of unit steps, with a +90-degree turn (resp. a -90-degree turn) at positions X=k' such that b_k = 1 (resp. b_k = 0) with k = k' mod m.

All positive terms of A002450 belong to this sequence.

Examples

			See illustration in Links section.
		

Links

• Rémy Sigrist, Illustration of initial terms

Crossrefs

Cf. A002450, A020330, A344022.

Programs

PARI

is(n) = { my (b=if (n, binary(n), [0]), d=1, s=[d], z=2*d); b=concat([b,b,b,b]); for (k=1, #b, if (b[k], d*=I, d/=I); if (setsearch(s, z+=d), return (0), s=setunion(s, [z]); z+=d)); return (1) }