A344145 - OEIS

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).

%I #9 May 14 2021 02:33:10

%S 2,9,10,12,35,37,38,41,42,44,49,50,52,56,139,141,142,147,149,150,153,

%T 154,156,163,165,166,169,170,172,177,178,180,184,197,198,201,202,204,

%U 209,210,212,216,226,228,232,555,557,558,563,565,566,569,570,587,589

%N 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).

%C 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.

%C All positive terms of A002450 belong to this sequence.

%H Rémy Sigrist, <a href="/A344145/a344145.png">Illustration of initial terms</a>

%e See illustration in Links section.

%o (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) }

%Y Cf. A002450, A020330, A344022.

%K nonn,base

%O 1,1

%A _Rémy Sigrist_, May 10 2021