A344022 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.

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, 28, 29, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 81, 82, 83, 84, 85

Offset: 1

Author

Rémy Sigrist, May 07 2021

Keywords

• nonn
• base

Comments

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

This sequence is infinite as it contains A000975 and A343183.

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

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

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

Examples

			See illustration in Links section.
		

Links

• Rémy Sigrist, Illustration of initial terms

Crossrefs

Cf. A000975, A006744, A166535, A258002, A255561, A255571, A343183, A344145.

Programs

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) }