A344022 - OEIS

%I #13 May 13 2021 14:33:26

%S 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,17,18,19,20,21,22,23,24,25,26,27,

%T 28,29,34,35,36,37,38,39,40,41,42,43,44,45,46,49,50,51,52,53,54,55,56,

%U 57,58,59,68,69,70,71,72,73,74,75,76,77,78,81,82,83,84,85

%N Numbers with binary expansion (b_1, ..., b_m) such that bending a strip of paper of length k+1 with an angle of +90 degrees (resp. -90 degrees) at position X=k when b_k = 1 (resp. b_k = 0) for k = 1..m yields a configuration where all edges are distinct.

%C All positive terms belong to A166535, but the reverse is not true (for example, A166535(96) = 136 does not belong to this sequence).

%C This sequence is infinite as it contains A000975 and A343183.

%C If m belongs to the sequence, then floor(m/2) also belongs to the sequence.

%C For any k > 0, the sequence contains A006744(k) positive terms with k binary digits.

%C This sequence has connections with A258002, A255561 and A255571: these sequences encode in binary nonoverlapping or noncrossing paths in the honeycomb lattice.

%H Rémy Sigrist, <a href="/A344022/a344022.png">Illustration of initial terms</a>

%e See illustration in Links section.

%o (PARI) is(n) = { my (b=binary(n), d=1, s=[d], z=2*d); 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. A000975, A006744, A166535, A258002, A255561, A255571, A343183, A344145.

%K nonn,base

%O 1,3

%A _Rémy Sigrist_, May 07 2021