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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.
2
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
1,3
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.
EXAMPLE
See illustration in Links section.
PROG
(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) }
KEYWORD
nonn,base
AUTHOR
Rémy Sigrist, May 07 2021
STATUS
approved