A343182 Binary word formed from first 2^n-1 terms of paper-folding sequence A014577, reversed and complemented.

0, 100, 1100100, 110110001100100, 1101100111001000110110001100100, 110110011100100111011000110010001101100111001000110110001100100

Offset

0,2

Comments

Take a sheet of paper, and fold the right edge up and onto the left edge. Do this n times. and unfold. Write a 0 for every valley and a 1 for every ridge, and read the sequence backwards.

a(7) is too large to include in the DATA section.

References

Chandler Davis and Donald E. Knuth, Number Representations and Dragon Curves -- I and II, Journal of Recreational Mathematics, volume 3, number 2, April 1970, pages 66-81, and number 3, July 1970, pages 133-149. Reprinted in Donald E. Knuth, Selected Papers on Fun and Games, CSLI Publications, 2010, pages 571-614.

Sunggye Lee, Jinsoo Kim, and Won Choi, Relation between folding and un-folding paper of rectangle and (0,1)-pattern [Korean], J. Korean Soc. Math. Ed. Ser. E, 23(3) (2009), 507-522.

Rémy Sigrist and N. J. A. Sloane, Two-Dimensional Paper-Folding, Manuscript in preparation, May 2021.

Links

Table of n, a(n) for n=0..5.

Chandler Davis and Donald E. Knuth, Number Representations and Dragon Curves, Journal of Recreational Mathematics, volume 3, number 2, April 1970, pages 66-81, and number 3, July 1970, pages 133-149. [Cached copy, with permission]

Crossrefs

When converted to base 10 we get A343183.

Cf. A014577. A variant of A343181.

Sequence in context: A185303 A139110 A265720 * A013855 A204576 A061890

Adjacent sequences: A343179 A343180 A343181 * A343183 A343184 A343185

Keyword

nonn

Author

N. J. A. Sloane, May 06 2021

Status

approved